Saralees Nadarajah

Current Organizations / Institutes

The organizations/institutes from the scholar's latest article

Research Subjects

Statistical Methods

Research Interests

Saralees Nadarajah has a total of 470 co-authors. Here are the top co-authors by number of shared publications:

Christopher Stroude Withers
Callaghan Innovation (Formerly Industrial Research Ltd.), 101 Allington Road, Wellington 6012, New Zealand, New Zealand
93 shared publications
Stephen Chan
American University of Sharjah, Sharjah, UAE
24 shared publications
Christopher S. Withers
15 shared publications
Emmanuel Afuecheta
Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia
12 shared publications
Mahdi Teimouri
Department of Statistics, Gonbad Kavous University, Gonbad Kavous, Iran
12 shared publications
Tibor K. Pogany
Institute of Applied Mathematics, Óbuda University, Budapest, Hungary
12 shared publications

Latest Publications

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Open Access
Google Scholar
- 12 November 2026
- Published by MDPI AG in Symmetry
Parametric Estimation in Censored Life-Testing: A Bayesian MAP Approach for Exponential and Weibull Distributions
by Christian Akrong Hesse, Emmanuel Dodzi Kpeglo, Dominic Buer Boyetey, Saralees Nadarajah, Evans Tee
This study evaluates the finite-sample performance of maximum likelihood estimation (MLE) and Bayesian maximum a posteriori (MAP) estimation for Exponential and Weibull lifetime distributions under Type-II right censoring. Data were simulated from both distributions, with each life-testing experiment ending after a specified number of failures among n units. Estimator performance was assessed using bias, mean squared error (MSE), root mean squared error (RMSE) and mean absolute error (MAE) under alternative prior specifications, including calibrated, weakly informative and deliberately misspecified priors. The results indicate that the relative performance of MAP and MLE depends on the quality of prior information and the degree of censoring. For the Weibull distribution, estimation performance also differed between the shape and scale parameters. An illustrative application to ball-bearing fatigue-life observations using their original right-censoring information further demonstrates posterior-mode estimation, prior sensitivity and Markov Chain Monte Carlo (MCMC) based uncertainty quantification. In summary, the location of the MAP estimate within the region of greatest posterior concentration is consistent with direct numerical maximisation of the joint posterior density.
Google Scholar
- 12 November 2026
- Published by MDPI AG in Symmetry
Open Access
Parametric Estimation in Censored Life-Testing: A Bayesian MAP Approach for Exponential and Weibull Distributions
by Christian Akrong Hesse, Emmanuel Dodzi Kpeglo, Dominic Buer Boyetey, Saralees Nadarajah, Evans Tee
This study evaluates the finite-sample performance of maximum likelihood estimation (MLE) and Bayesian maximum a posteriori (MAP) estimation for Exponential and Weibull lifetime distributions under Type-II right censoring. Data were simulated from both distributions, with each life-testing experiment ending after a specified number of failures among n units. Estimator performance was assessed using bias, mean squared error (MSE), root mean squared error (RMSE) and mean absolute error (MAE) under alternative prior specifications, including calibrated, weakly informative and deliberately misspecified priors. The results indicate that the relative performance of MAP and MLE depends on the quality of prior information and the degree of censoring. For the Weibull distribution, estimation performance also differed between the shape and scale parameters. An illustrative application to ball-bearing fatigue-life observations using their original right-censoring information further demonstrates posterior-mode estimation, prior sensitivity and Markov Chain Monte Carlo (MCMC) based uncertainty quantification. In summary, the location of the MAP estimate within the region of greatest posterior concentration is consistent with direct numerical maximisation of the joint posterior density.
Open Access
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Google Scholar
- 9 November 2026
- Published by MDPI AG in Mathematics
A Discrete GEV Distribution
by Adamu Abubakar Umar, Saralees Nadarajah
Annual maximum data are frequently recorded as integers, yet they are routinely modeled with the continuous generalized extreme value (GEV) distribution. We study the discrete GEV distribution of Dkengne et al. (2016), which is the distribution of the integer part of a continuous GEV random variable, and we provide a systematic treatment of its distributional, inferential and finite-sample properties. The model retains the location, scale and shape parameters of its continuous counterpart and contains the discrete Gumbel, discrete Fréchet and discrete (reversed) Weibull distributions as particular cases. We give the support (including the endpoint cases), the probability mass and cumulative distribution functions, their tail behavior, moments, the quantile function, and quantile-based measures of skewness and kurtosis. For maximum likelihood estimation, we identify the subsets of the parameter space on which the support is locally fixed, show that the model is differentiable in quadratic mean on a larger set that also contains integer endpoints when $β > - \frac{1}{2}$ , and state the resulting asymptotic normality. We also show that flooring, ceiling and rounding of a GEV variable all lead to the same discrete family up to a shift in location. Simulation studies examine the finite-sample performance of the estimators and compare the discrete GEV with the continuous GEV fitted to the integer values under several observation mechanisms, including block maxima of integer counts. Applications to annual maximum wind speeds at Lisbon and annual maximum temperatures at Oxford are analyzed with discrete versions of the Kolmogorov–Smirnov, Cramér–von Mises and Anderson–Darling statistics calibrated by a parametric bootstrap.
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Google Scholar
- 9 November 2026
- Published by MDPI AG in Mathematics
Open Access
A Discrete GEV Distribution
by Adamu Abubakar Umar, Saralees Nadarajah
Annual maximum data are frequently recorded as integers, yet they are routinely modeled with the continuous generalized extreme value (GEV) distribution. We study the discrete GEV distribution of Dkengne et al. (2016), which is the distribution of the integer part of a continuous GEV random variable, and we provide a systematic treatment of its distributional, inferential and finite-sample properties. The model retains the location, scale and shape parameters of its continuous counterpart and contains the discrete Gumbel, discrete Fréchet and discrete (reversed) Weibull distributions as particular cases. We give the support (including the endpoint cases), the probability mass and cumulative distribution functions, their tail behavior, moments, the quantile function, and quantile-based measures of skewness and kurtosis. For maximum likelihood estimation, we identify the subsets of the parameter space on which the support is locally fixed, show that the model is differentiable in quadratic mean on a larger set that also contains integer endpoints when $β > - \frac{1}{2}$ , and state the resulting asymptotic normality. We also show that flooring, ceiling and rounding of a GEV variable all lead to the same discrete family up to a shift in location. Simulation studies examine the finite-sample performance of the estimators and compare the discrete GEV with the continuous GEV fitted to the integer values under several observation mechanisms, including block maxima of integer counts. Applications to annual maximum wind speeds at Lisbon and annual maximum temperatures at Oxford are analyzed with discrete versions of the Kolmogorov–Smirnov, Cramér–von Mises and Anderson–Darling statistics calibrated by a parametric bootstrap.
Open Access
Website
Google Scholar
- 6 November 2026
- Published by MDPI AG in AppliedMath
Benchmark-Adjusted Stochastic Valuation of Real Estate Assets: Evidence from Ghana
by Christian A. Hesse, Dominic B. Boyetey, Emmanuel D. Kpeglo, Saralees Nadarajah, Evans Tee
This study develops a benchmark-relative application of geometric Brownian motion (GBM) for evaluating the capital-value performance of real estate under uncertainty. It introduces a valuation-regime taxonomy that distinguishes the growth conditions for benchmark-adjusted mean, median, and modal property values and links them to benchmark underperformance and downside risk over alternative holding horizons. Using a compiled annual median residential property-price series for Accra and Tema (2016–2026), the Ghanaian application illustrates how nominal property appreciation can coexist with deteriorating benchmark-relative performance when appreciation is insufficient relative to the selected investment benchmark. The analysis further demonstrates that expected and median benchmark-adjusted values may exhibit opposing growth patterns, while the probability of benchmark underperformance depends on the interaction among appreciation, benchmark return, volatility, and investment horizon. Rental-yield sensitivity further shows that relatively small positive net yields can alter the classification. The proposed approach provides a probabilistic assessment of benchmark-relative capital-value performance, complementing conventional nominal growth projections.
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Google Scholar
- 6 November 2026
- Published by MDPI AG in AppliedMath
Open Access
Benchmark-Adjusted Stochastic Valuation of Real Estate Assets: Evidence from Ghana
by Christian A. Hesse, Dominic B. Boyetey, Emmanuel D. Kpeglo, Saralees Nadarajah, Evans Tee
This study develops a benchmark-relative application of geometric Brownian motion (GBM) for evaluating the capital-value performance of real estate under uncertainty. It introduces a valuation-regime taxonomy that distinguishes the growth conditions for benchmark-adjusted mean, median, and modal property values and links them to benchmark underperformance and downside risk over alternative holding horizons. Using a compiled annual median residential property-price series for Accra and Tema (2016–2026), the Ghanaian application illustrates how nominal property appreciation can coexist with deteriorating benchmark-relative performance when appreciation is insufficient relative to the selected investment benchmark. The analysis further demonstrates that expected and median benchmark-adjusted values may exhibit opposing growth patterns, while the probability of benchmark underperformance depends on the interaction among appreciation, benchmark return, volatility, and investment horizon. Rental-yield sensitivity further shows that relatively small positive net yields can alter the classification. The proposed approach provides a probabilistic assessment of benchmark-relative capital-value performance, complementing conventional nominal growth projections.
Open Access
Website
Google Scholar
- 21 October 2026
- Published by MDPI AG in Axioms
The Derivatives of the Inverse of a One-to-One Multivariate Function
by Christopher S. Withers, Saralees Nadarajah, Paul Teal
Consider a multivariate function f that maps an open region of $R^{p}$ into $R^{p}$ , together with its inverse function. This paper presents a general method for obtaining the partial derivatives of the inverse function, of any order, expressed in terms of the partial derivatives of the inverse of the Jacobian matrix of f. The results are local. They require only that f have continuous partial derivatives up to the order of interest in a neighbourhood of a point, and a nonsingular Jacobian at that point, so global one-to-one-ness is not needed. A recursion for the derivatives of the inverse is proved by induction. Explicit formulas are derived for all partial derivatives up to the fourth order, both for the inverse function and for the inverse Jacobian. The symmetry of the mixed partial derivatives of the inverse is established. The computational cost is discussed: the explicit formulas grow factorially with the order, whereas a Leibniz-type recursion gives polynomial cost for numerical evaluation. A recursive scheme implemented in Python using symbolic computation is provided for derivatives of arbitrary order, together with a program that verifies the explicit formulas independently against direct differentiation. The univariate case, published previously by Withers, Nadarajah and Teal in the journal Axioms, is reviewed first, recovering known results expressed in terms of Bell polynomials. The method is illustrated by worked examples in two dimensions. Its use in mathematical statistics is shown by casting maximum likelihood estimation in canonical exponential families, including a canonical regression setting, in the framework of the paper, and by deriving explicitly the bias-corrected maximum likelihood estimator with bias $O (n^{- 2})$ , which is checked against an exact calculation for the normal distribution.
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- 21 October 2026
- Published by MDPI AG in Axioms
Open Access
The Derivatives of the Inverse of a One-to-One Multivariate Function
by Christopher S. Withers, Saralees Nadarajah, Paul Teal
Consider a multivariate function f that maps an open region of $R^{p}$ into $R^{p}$ , together with its inverse function. This paper presents a general method for obtaining the partial derivatives of the inverse function, of any order, expressed in terms of the partial derivatives of the inverse of the Jacobian matrix of f. The results are local. They require only that f have continuous partial derivatives up to the order of interest in a neighbourhood of a point, and a nonsingular Jacobian at that point, so global one-to-one-ness is not needed. A recursion for the derivatives of the inverse is proved by induction. Explicit formulas are derived for all partial derivatives up to the fourth order, both for the inverse function and for the inverse Jacobian. The symmetry of the mixed partial derivatives of the inverse is established. The computational cost is discussed: the explicit formulas grow factorially with the order, whereas a Leibniz-type recursion gives polynomial cost for numerical evaluation. A recursive scheme implemented in Python using symbolic computation is provided for derivatives of arbitrary order, together with a program that verifies the explicit formulas independently against direct differentiation. The univariate case, published previously by Withers, Nadarajah and Teal in the journal Axioms, is reviewed first, recovering known results expressed in terms of Bell polynomials. The method is illustrated by worked examples in two dimensions. Its use in mathematical statistics is shown by casting maximum likelihood estimation in canonical exponential families, including a canonical regression setting, in the framework of the paper, and by deriving explicitly the bias-corrected maximum likelihood estimator with bias $O (n^{- 2})$ , which is checked against an exact calculation for the normal distribution.
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Google Scholar
- 15 October 2026
- Published by World Scientific Pub Co Pte Ltd in International Journal of Reliability, Quality and Safety Engineering
On the Generalized Gompertz and Reversed Generalized Gompertz Distributions
by Saralees Nadarajah, Talal Kurdi, Tibor K. Pogány
This paper presents a comprehensive mathematical and statistical analysis of the generalized Gompertz and reversed generalized Gompertz distributions, introduced by [W. J. Willemse and R. Kaas, Rational reconstruction of frailty-based mortality models by a generalization of Gompertz’ law of mortality, Insur. Math. Econ. 40 (2007) 468–484]. A wide range of mathematical properties is rigorously derived, including the shapes of the density functions, moment generating and characteristic functions, ordinary and conditional moments, quantiles, mean deviations, mean residual life, expected inactive time, inequality curves (Lorenz, Bonferroni, Zenga), order statistics, extreme value limits, and Kullback–Leibler divergence measures (Shannon, Rényi, Tsallis, Kullback–Leibler) and the distributions of the sums and differences of generalized Gompertz and reversed generalized Gompertz random variables. The maximum likelihood method is employed for parameter estimation, and the asymptotic properties of the estimators are established. A detailed simulation study demonstrates the finite-sample performance of the estimators, confirming their consistency, low bias, and adequate coverage probabilities across various parameter configurations and sample sizes. Finally, the applicability of both distributions is illustrated using a real data set on lifetimes of glass capacitors, where both models provide satisfactory fits and outperform a range of standard competitors. The results indicate that the distributions are flexible and theoretically well-founded models suitable for applications in reliability.
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Google Scholar
- 15 October 2026
- Published by World Scientific Pub Co Pte Ltd in International Journal of Reliability, Quality and Safety Engineering
On the Generalized Gompertz and Reversed Generalized Gompertz Distributions
by Saralees Nadarajah, Talal Kurdi, Tibor K. Pogány
This paper presents a comprehensive mathematical and statistical analysis of the generalized Gompertz and reversed generalized Gompertz distributions, introduced by [W. J. Willemse and R. Kaas, Rational reconstruction of frailty-based mortality models by a generalization of Gompertz’ law of mortality, Insur. Math. Econ. 40 (2007) 468–484]. A wide range of mathematical properties is rigorously derived, including the shapes of the density functions, moment generating and characteristic functions, ordinary and conditional moments, quantiles, mean deviations, mean residual life, expected inactive time, inequality curves (Lorenz, Bonferroni, Zenga), order statistics, extreme value limits, and Kullback–Leibler divergence measures (Shannon, Rényi, Tsallis, Kullback–Leibler) and the distributions of the sums and differences of generalized Gompertz and reversed generalized Gompertz random variables. The maximum likelihood method is employed for parameter estimation, and the asymptotic properties of the estimators are established. A detailed simulation study demonstrates the finite-sample performance of the estimators, confirming their consistency, low bias, and adequate coverage probabilities across various parameter configurations and sample sizes. Finally, the applicability of both distributions is illustrated using a real data set on lifetimes of glass capacitors, where both models provide satisfactory fits and outperform a range of standard competitors. The results indicate that the distributions are flexible and theoretically well-founded models suitable for applications in reliability.
Open Access
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Google Scholar
Cited by 1
- 14 October 2026
- Published by MDPI AG in Fractal and Fractional
Conditional Predictive Gains from Multiscale Networks for a Chinese Equity Opening
by Yuancheng Si, Yunqian Wei, Saralees Nadarajah
Chinese equity indices open after foreign markets have already supplied part of the day’s information. We ask whether multiscale dependence networks improve opening forecasts conditionally on states observable before the mainland opening. Daily prices from 2010 to July 2026 support 2081 evaluation dates per index. The design distinguishes incomplete local records, stale news, index launch availability, and accumulated foreign changes during domestic closures. A fixed LightGBM model adds 57 fluctuation order dependent DCCA features to the same feasible Raw information set. Six economic state partitions, matched benchmarks, and chronological rule assessment distinguish a useful representation from unrestricted model superiority. The clearest additional evidence concerns Shanghai’s absolute prediction error. On 1036 mornings with above median foreign news disagreement, mean absolute error falls from 25.90 to 24.83 basis points, a 4.12 percent reduction; the pointwise 95 percent block interval for the 1.07-basis-point gain is [0.64, 1.52]. This secondary absolute-loss comparison has Holm adjusted $p = 0.0094$ across 468 comparisons and $p = 0.0296$ in a wider 1482 test audit. Its later period estimate remains positive but does not pass the corresponding multiplicity adjustment. High-minus-low gain differences also do not establish unique state dependence. Squared-error and extreme probability comparisons do not show general network dominance, and forward applied gates do not deliver an adjusted significant advantage. The evidence supports a loss- and benchmark specific conditional increment, rather than an identified multifractal mechanism or a universally preferable risk model.
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Google Scholar
- 14 October 2026
- Published by MDPI AG in Fractal and Fractional
Open Access
Conditional Predictive Gains from Multiscale Networks for a Chinese Equity Opening
by Yuancheng Si, Yunqian Wei, Saralees Nadarajah
Chinese equity indices open after foreign markets have already supplied part of the day’s information. We ask whether multiscale dependence networks improve opening forecasts conditionally on states observable before the mainland opening. Daily prices from 2010 to July 2026 support 2081 evaluation dates per index. The design distinguishes incomplete local records, stale news, index launch availability, and accumulated foreign changes during domestic closures. A fixed LightGBM model adds 57 fluctuation order dependent DCCA features to the same feasible Raw information set. Six economic state partitions, matched benchmarks, and chronological rule assessment distinguish a useful representation from unrestricted model superiority. The clearest additional evidence concerns Shanghai’s absolute prediction error. On 1036 mornings with above median foreign news disagreement, mean absolute error falls from 25.90 to 24.83 basis points, a 4.12 percent reduction; the pointwise 95 percent block interval for the 1.07-basis-point gain is [0.64, 1.52]. This secondary absolute-loss comparison has Holm adjusted $p = 0.0094$ across 468 comparisons and $p = 0.0296$ in a wider 1482 test audit. Its later period estimate remains positive but does not pass the corresponding multiplicity adjustment. High-minus-low gain differences also do not establish unique state dependence. Squared-error and extreme probability comparisons do not show general network dominance, and forward applied gates do not deliver an adjusted significant advantage. The evidence supports a loss- and benchmark specific conditional increment, rather than an identified multifractal mechanism or a universally preferable risk model.
Cited by 1
Open Access
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Google Scholar
- 7 October 2026
- Published by Springer Nature in Discover Sustainability
Spatiotemporal dynamics and fatality risk patterns of road traffic crashes in Nigeria (2020–2024)
by Mukhtar Hassan, Saralees Nadarajah, Isqeel Ogunsola
Background: Road traffic crashes pose a significant public health issue in Nigeria, but there is limited national-level analysis of their spatial and temporal patterns. This study investigates the distribution, temporal trends, and severity of reported road traffic crashes across Nigeria’s 36 states and the Federal Capital Territory (FCT). Methods: We conducted a retrospective longitudinal study analysing quarterly Federal Road Safety Corps (FRSC) crash data across 37 jurisdictions from Q4 2020 to Q1 2024, covering 14 quarters with 518 state-quarter observations. Key indicators included the fatality rate (deaths per crash), casualty rate, and severity index. State-level comparisons summarised crash burden and lethality, and, when population data were available, measured crashes and fatalities per 100,000 residents. Exploratory trend projections were produced using an ensemble of a linear (OLS) trend, exponential smoothing (ETS, α = 0.7), and ARIMA (0,1,0) with drift. Results: Showed that crashes peaked at 13,656 in 2022, with 6456 deaths, and then declined by 22.3% in 2023. The fatality rate per crash stayed steady between 0.47 and 0.48 deaths from 2021 to 2023, despite decreasing crash numbers. Geographically, crash burden was concentrated: the FCT had the highest crash count (4852) but a low fatality rate (0.224), while northern states such as Sokoto, Katsina, and Kaduna had higher death rates per crash with fewer crashes. After adjusting for population, the ranking of states changed, showing that some of the burden is due to population size. Speed violations and vehicle-related issues were common factors noted by officers. Projections suggest that quarterly crash numbers will likely remain high in the short term, though uncertainty is increasing over time. Conclusion: The results emphasise the importance of shifting to risk-based road safety strategies in Nigeria, with a primary focus on speed regulation, vehicle safety checks, and enhanced emergency response systems. These recommendations are inferred policy implications of the observed patterns rather than evidence of intervention effectiveness.
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- 7 October 2026
- Published by Springer Nature in Discover Sustainability
Open Access
Spatiotemporal dynamics and fatality risk patterns of road traffic crashes in Nigeria (2020–2024)
by Mukhtar Hassan, Saralees Nadarajah, Isqeel Ogunsola
Background: Road traffic crashes pose a significant public health issue in Nigeria, but there is limited national-level analysis of their spatial and temporal patterns. This study investigates the distribution, temporal trends, and severity of reported road traffic crashes across Nigeria’s 36 states and the Federal Capital Territory (FCT). Methods: We conducted a retrospective longitudinal study analysing quarterly Federal Road Safety Corps (FRSC) crash data across 37 jurisdictions from Q4 2020 to Q1 2024, covering 14 quarters with 518 state-quarter observations. Key indicators included the fatality rate (deaths per crash), casualty rate, and severity index. State-level comparisons summarised crash burden and lethality, and, when population data were available, measured crashes and fatalities per 100,000 residents. Exploratory trend projections were produced using an ensemble of a linear (OLS) trend, exponential smoothing (ETS, α = 0.7), and ARIMA (0,1,0) with drift. Results: Showed that crashes peaked at 13,656 in 2022, with 6456 deaths, and then declined by 22.3% in 2023. The fatality rate per crash stayed steady between 0.47 and 0.48 deaths from 2021 to 2023, despite decreasing crash numbers. Geographically, crash burden was concentrated: the FCT had the highest crash count (4852) but a low fatality rate (0.224), while northern states such as Sokoto, Katsina, and Kaduna had higher death rates per crash with fewer crashes. After adjusting for population, the ranking of states changed, showing that some of the burden is due to population size. Speed violations and vehicle-related issues were common factors noted by officers. Projections suggest that quarterly crash numbers will likely remain high in the short term, though uncertainty is increasing over time. Conclusion: The results emphasise the importance of shifting to risk-based road safety strategies in Nigeria, with a primary focus on speed regulation, vehicle safety checks, and enhanced emergency response systems. These recommendations are inferred policy implications of the observed patterns rather than evidence of intervention effectiveness.
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- 30 September 2026
- Published by Springer Nature in Computational Economics
Intraday Timing of Bitcoin Price and Volume Extremes: A Bayesian Directional Statistics Approach
by Talal Kurdi, Saralees Nadarajah
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- 30 September 2026
- Published by Springer Nature in Computational Economics
Intraday Timing of Bitcoin Price and Volume Extremes: A Bayesian Directional Statistics Approach
by Talal Kurdi, Saralees Nadarajah
Open Access
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- 22 September 2026
- Published by Springer Nature in Scientific Reports
A new family of distributions for circular data
by Saralees Nadarajah, William Bell
A new method for constructing distributions for circular data is proposed. The method is based on piecewise probability density functions, in which two beta-type components are joined at a data-driven cut-point subject to continuity and periodicity conditions. The resulting family of distributions admits closed-form expressions for the cumulative distribution function, trigonometric moments, mean angle, mean resultant length, circular variance, Rényi entropy and Shannon entropy, and is simpler to compute than existing models since it relies only on the incomplete beta function, a widely supported special function. Maximum likelihood estimation is developed in detail, and the finite-sample behaviour of the estimators is examined through an extensive simulation study covering five representative parameter configurations. The proposed distribution is fitted to five real circular data sets and compared with seven competing models, including the distributions due to Jones and Pewsey ¹⁴ and Kato and Jones ¹⁵ . In every case, the proposed distribution attains the smallest AIC and BIC values and the largest Kuiper test p -value, providing consistent evidence of superior fit over all competitors.
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- 22 September 2026
- Published by Springer Nature in Scientific Reports
Open Access
A new family of distributions for circular data
by Saralees Nadarajah, William Bell
A new method for constructing distributions for circular data is proposed. The method is based on piecewise probability density functions, in which two beta-type components are joined at a data-driven cut-point subject to continuity and periodicity conditions. The resulting family of distributions admits closed-form expressions for the cumulative distribution function, trigonometric moments, mean angle, mean resultant length, circular variance, Rényi entropy and Shannon entropy, and is simpler to compute than existing models since it relies only on the incomplete beta function, a widely supported special function. Maximum likelihood estimation is developed in detail, and the finite-sample behaviour of the estimators is examined through an extensive simulation study covering five representative parameter configurations. The proposed distribution is fitted to five real circular data sets and compared with seven competing models, including the distributions due to Jones and Pewsey ¹⁴ and Kato and Jones ¹⁵ . In every case, the proposed distribution attains the smallest AIC and BIC values and the largest Kuiper test p -value, providing consistent evidence of superior fit over all competitors.
Open Access
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- 10 September 2026
- Published by Wiley in Public Health Challenges
Determinants of the Number of Tetanus‐Toxoid Injections Before Birth Among Pregnant Women in Somalia: A Multilevel Analysis
by Jama Mohamed, Hamse Mohamed Amoud, Ahmed Ismail Mohamed, Abdisalam Hassan Muse, Azizur Rahman, Saralees Nadarajah
Background: Maternal and neonatal tetanus remains a major public health concern in Somalia, where low immunization coverage contributes to preventable mortality. Despite global progress, Somalia continues to report suboptimal tetanus‐toxoid (TT) vaccine uptake due to conflict, weak health systems, and socioeconomic barriers. This study examined multilevel factors associated with the number of TT injections before birth among Somali women. Methods: We analyzed data from the Somali Health and Demographic Survey (2020), including 4841 pregnant women aged 15–49. A mixed‐effects negative binomial regression model addressed overdispersion, excess zeros, and hierarchical structure (region and residence). Model fit was assessed using Akaike (AIC) and Bayesian (BIC) information criteria. Results: Only 32.6% of women received at least one TT injection, whereas 67.4% received none. Higher TT uptake was associated with older age (IRR = 1.62; 95% CI = 1.09–2.42), higher wealth (IRR = 1.49; 95% CI = 1.01–2.18), prior vaccination (IRR = 1.76; 95% CI = 1.44–2.16), antenatal care visits (IRR = 1.02; 95% CI = 1.01–1.04), employment (IRR = 1.41; 95% CI = 1.00–1.97), clinic deliveries (IRR = 1.23; 95% CI = 1.01–1.50), and health insurance (IRR = 5.24; 95% CI = 1.04–26.47). Conversely, zero uptake was more likely among nomadic women (AOR = 1.40; 95% CI = 1.06–1.85), those with no prior vaccination (AOR = 3.64; 95% CI = 2.76–4.80), home deliveries (AOR = 1.42; 95% CI = 1.18–1.71), no phone ownership (AOR = 1.31; 95% CI = 1.02–1.68), and women whose husbands lacked education (AOR = 1.27; 95% CI = 1.02–1.58). Conclusion: TT vaccine coverage among pregnant women in Somalia remains critically low and is shaped by socioeconomic inequities, healthcare access, and household decision‐making. Strengthening antenatal care integration, targeted outreach for nomadic populations, economic empowerment, health education, and expanding insurance coverage are essential to improve maternal immunization and eliminate neonatal tetanus.
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- 10 September 2026
- Published by Wiley in Public Health Challenges
Open Access
Determinants of the Number of Tetanus‐Toxoid Injections Before Birth Among Pregnant Women in Somalia: A Multilevel Analysis
by Jama Mohamed, Hamse Mohamed Amoud, Ahmed Ismail Mohamed, Abdisalam Hassan Muse, Azizur Rahman, Saralees Nadarajah
Background: Maternal and neonatal tetanus remains a major public health concern in Somalia, where low immunization coverage contributes to preventable mortality. Despite global progress, Somalia continues to report suboptimal tetanus‐toxoid (TT) vaccine uptake due to conflict, weak health systems, and socioeconomic barriers. This study examined multilevel factors associated with the number of TT injections before birth among Somali women. Methods: We analyzed data from the Somali Health and Demographic Survey (2020), including 4841 pregnant women aged 15–49. A mixed‐effects negative binomial regression model addressed overdispersion, excess zeros, and hierarchical structure (region and residence). Model fit was assessed using Akaike (AIC) and Bayesian (BIC) information criteria. Results: Only 32.6% of women received at least one TT injection, whereas 67.4% received none. Higher TT uptake was associated with older age (IRR = 1.62; 95% CI = 1.09–2.42), higher wealth (IRR = 1.49; 95% CI = 1.01–2.18), prior vaccination (IRR = 1.76; 95% CI = 1.44–2.16), antenatal care visits (IRR = 1.02; 95% CI = 1.01–1.04), employment (IRR = 1.41; 95% CI = 1.00–1.97), clinic deliveries (IRR = 1.23; 95% CI = 1.01–1.50), and health insurance (IRR = 5.24; 95% CI = 1.04–26.47). Conversely, zero uptake was more likely among nomadic women (AOR = 1.40; 95% CI = 1.06–1.85), those with no prior vaccination (AOR = 3.64; 95% CI = 2.76–4.80), home deliveries (AOR = 1.42; 95% CI = 1.18–1.71), no phone ownership (AOR = 1.31; 95% CI = 1.02–1.68), and women whose husbands lacked education (AOR = 1.27; 95% CI = 1.02–1.58). Conclusion: TT vaccine coverage among pregnant women in Somalia remains critically low and is shaped by socioeconomic inequities, healthcare access, and household decision‐making. Strengthening antenatal care integration, targeted outreach for nomadic populations, economic empowerment, health education, and expanding insurance coverage are essential to improve maternal immunization and eliminate neonatal tetanus.

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