Suleman Nasiru

A new family of distributions based on the bounded Marshall-Olkin exponential distribution. The new distribution known as the bounded Marshall-Olkin extended exponentially generated family of distributions. Various statistical properties, including the quantile function, characteristic function, moments and moment-generating function were derived for this new family. The distribution parameters were estimated using the maximum likelihood, ordinary least squares, and Cramér-von Mises procedures. In addition, the study explores three special distributions derived from the newly bounded Marshall-Olkin extended exponential-generated family. The hazard rates of these special distributions show their suitability for datasets exhibiting diverse non-monotonic failure rates. Monte Carlo simulations demonstrated the consistency of the estimators, with the maximum likelihood estimator showing superior performance compared to the other estimators. A location-scale regression model was conducted with data on long-term interest against direct foreign investment. It was observed that long-term interest rates positively affect foreign direct investment with a 5% confidence level of significance for bounded Marshall-Olkin extended exponential Weibull and all the competing location-scale regression models.

Developing flexible probability distributions capable of capturing complex features observed in lifetime data remains a fundamental challenge in statistical modeling. The limitations of classical probability distributions in adequately modeling varying degrees of skewness, heavy‐tailed behavior, and nonmonotonic failure rates have motivated the development of more flexible distributional families based on diverse transformation mechanisms. This paper introduces the alpha power new exponentiated family (APNEF) of distributions, a unified framework that integrates two transformation mechanisms: the new exponentiation transformation and the alpha power transformation. The proposed family extends baseline distributions through multiple shape parameters, enabling flexibility in capturing complex data structures while maintaining computational tractability. We derive key statistical properties of the APNEF, including the quantile function, noncentral and incomplete moments, the Rényi entropy, and the Lorenz and Bonferroni inequality curves. A suite of estimation procedures is developed and assessed via Monte Carlo simulation, evaluating finite‐sample performance and consistency and offering guidance on estimator choice. We extend the APNEF to a log‐location‐scale regression framework to facilitate its application in regression settings. The resulting model falls within the accelerated failure time class, with covariates entering linearly on the log‐response scale and a shape parameter determining the form of the error term. The theoretical and empirical effectiveness of the proposed family is demonstrated through applications to lifetime datasets, where the alpha power new Weibull distribution, a member of the APNEF family, consistently outperforms numerous competing models. The findings establish APNEF as a valuable and flexible framework for statistical inference in reliability analysis, survival studies, and other applied domains.

We introduce the Weibull–Odd Perks distribution (WOPD), a three‐parameter lifetime model obtained by composing the odds function of the Perks distribution with the Weibull‐ G generator. The construction admits a structural reduction thus if X ~ WOPD( ψ , υ , γ ), then e ^{υ X} − 1 follows a two‐parameter Weibull law, and this identity drives the entire analytic development. Exploiting it, we obtain the quantile function in a closed form, together with exact series representations of the r ‐th raw moment expressed through the unsigned Stirling numbers of the first kind and parametric derivatives of the upper incomplete gamma function, and an equivalent single‐integral form well suited to Gauss–Laguerre quadrature. The Lorenz and Bonferroni curves are derived as lower‐incomplete‐gamma series, the Shannon entropy is reduced to a unit‐exponential expectation involving the Euler–Mascheroni constant, and the Rényi entropy is obtained in a closed form. We further characterize the shape regimes of the model, showing that the density admits unimodal, right‐skewed, left‐skewed, and approximately symmetric forms while the hazard rate accommodates increasing, decreasing, bathtub, and unimodal behavior. Seven frequentist estimators, namely, maximum likelihood, Anderson–Darling, Cramér–von Mises, maximum product of spacings, ordinary and weighted least squares, and percentile estimation, are compared through Monte Carlo experiments that establish the consistency and finite‐sample accuracy of the estimation procedure. A log‐location‐scale regression extension is developed and validated via Cox–Snell residual diagnostics. In applications to two real lifetime datasets, the WOPD is preferred over eight competing models on all goodness‐of‐fit and information criteria for one dataset and matches the fit of a four‐parameter alternative with one fewer parameter for the other; a further application to hypertension survival data from Ghana illustrates the regression model in a biomedical setting with covariates.

Sustainable Development Goal 3 has established clear targets to combat noncommunicable diseases (NCDs) such as cancer and cardiovascular diseases among others by the year 2030. A handy technique to study cancer progression is to analyze patient survival over time to obtain precise results to enable for the establishment of cancer control mechanisms. The use of cure rate models for analyzing survival data with cured elements is more desirable than the standard survival analysis models. This study formulated the Poisson‐gamma trigonometric families of cure rate models under the competing risks setup based on the Poisson‐gamma cure rate model and the trigonometric families of distributions. Four special models are obtained from the proposed families. Maximum likelihood estimation technique was utilized for estimating the parameters of the developed families. The cure rate families are parameterized in terms of the cure term and diverse link functions such as logit, cauchit, Aranda‐Ordaz, and skewed logit are utilized to determine the effects of covariates. Monte Carlo simulation study was conducted to determine the behavior of the maximum likelihood estimator. The applications of the proposed models were finally established using myeloma and acute myeloid leukemia datasets. The study revealed that the proposed cure rate models provided better fit to the cancer datasets compared with the candidate models.

While significant progress has been made in face recognition under individual environmental constraints, comprehensive approaches that address multiple simultaneous challenges—such as occlusion and pose variation—remain relatively scarce in the literature. Most existing recognition models are tailored to mitigate specific conditions in isolation, thereby limiting their generalizability in real‐world, unconstrained environments. Concurrently, transfer learning has emerged as a dominant paradigm, with pretrained convolutional neural networks (CNNs) being fine‐tuned for downstream face recognition tasks due to their efficiency and superior performance. Despite the inherent robustness of deep learning models to certain distortions, their effectiveness can be substantially improved through appropriate preprocessing strategies, especially under compound constraints. In this study, we introduce a dual‐stage frequency‐domain preprocessing framework based on the discrete cosine transform (DCT) and fast Fourier transform (FFT), designed to enhance the performance of a hybrid SqueezeNet–PCA–SVM architecture for face recognition under dual constraints—synthetic occlusion and head tilt. To simulate real‐world variability, test images were artificially occluded at 20% and 30% levels and then reconstructed using a statistical imputation technique known as multiple imputation by chained equations (MICE). Experimental results show that integrating the DCT–FFT preprocessing pipeline with the SqueezeNet–PCA–SVM model significantly boosts recognition accuracy, from 70% to 76.25% at 20% occlusion recovery and from 32.5% to 63.75% at 30%. These findings affirm the efficacy of DCT–FFT as a noise‐reduction mechanism that enhances the discriminative quality of imputed images and underscore its value as a preprocessing enhancement for deep learning–based face recognition systems operating in multiconstrained environments.

Novel parametric and semiparametric regression models are proposed in this study based on the four‐parameter tan exponentiated odd log‐logistic Weibull distribution. Some statistical properties of the new distribution are derived. The parameters of the models are estimated through a maximum likelihood approach. Monte Carlo simulations for some finite parameter values and sample sizes under different censoring percentages empirically revealed the consistency of the estimators. The robustness of the proposed regression models over other regression models under the GAMLSS framework is demonstrated by means of censored and uncensored data. Thus, the new models can be viewed as intriguing alternatives for future work on real data.

A unique one‐parameter discrete distribution, known as the Poisson Two‐Sum Chris–Jerry distribution, is proposed in this study. The structural properties of the contemporary distribution, such as index of dispersion, moments, and probability‐generating function, are determined. To obtain the estimates of the parameter, the maximum likelihood estimation procedure is used. The performance of the estimation technique on finite samples is assessed through a comprehensive simulation study. The formulated distribution is further used to develop an integer autoregressive process for modeling autocorrelated count data. The usefulness of the new distribution and its autoregressive process are demonstrated by modeling some count data and their performances compared with other existing competing discrete distributions. The results show that both the distribution and its autoregressive process can serve as alternative models for count data modeling.

In recent times, researchers have resorted to using trigonometric and error function‐generated families of distributions for extending baseline distributions due to their parsimonious and flexible nature. The study proposed the sine error function‐generated family of distributions and derived the statistical properties of the proposed family. Four special models based on the proposed family are presented. The hazard rate functions of the special models exhibit various forms such as increasing, decreasing and upside‐down bathtub shapes. The study estimated the parameters of the formulated family using four estimation techniques, and a simulation study was conducted to assess the behaviour of the estimators. The study illustrated the applications of the proposed family using two real‐life datasets, and it was revealed that the sine error function Weibull distribution provided the best fit to the datasets in all cases.

This study presents a novel suite of discrete trigonometric Burr–Hatke distributions, encompassing the discrete tangent Burr–Hatke (DTBH), discrete sine Burr–Hatke (DSBH), discrete cosine Burr–Hatke (DCBH), and discrete type II tangent Burr–Hatke (DTIITBH) distributions to model count data with overdispersion and right‐skewed characteristics commonly observed in count data. Empirical analyses using three real‐world datasets show that the DTBH and DCBH models, respectively, outperform established alternatives according to model evaluation metrics. This research further proposes their integration into time series and zero‐truncated frameworks. A first‐order integer‐valued autoregressive process (INAR(1)) utilizing negative binomial thinning and DCBH innovations is formulated, termed the NBINAR (1)‐DCBHD model. The proposed NBINAR (1)‐DCBHD model delivers superior fit and predictive accuracy, validated by lowest AIC, BIC, RMSE, and satisfactory diagnostic tests. Additionally, to address zero‐truncated count scenarios, the zero‐truncated discrete cosine Burr–Hatke distribution (ZTDCBHD) is proposed and shown to outperform other existing distributions. Estimating population size with the Horvitz–Thompson estimator under the ZTDCBHD yields improved estimates for hidden populations across two different datasets and further validated using a dataset with known population size. The study establishes that the proposed discrete trigonometric Burr–Hatke models present a flexible option for modeling count data in time series and population estimation settings.

Modeling data that falls within the [0,1] domain is a huge task in most scientific disciplines. This is because most classical distributions do not address the issues of complex data shapes as well as managing the dynamism of extreme quantiles. The study thus developed the secant‐based extension of the unit Gompertz distribution; this distribution is a parametric and nonlinear quantile regression (QR) modeling strategy, which comes without the addition of parameters to the baseline distribution. The motivation behind this new approach lies in its use of trigonometric family of distributions, which enhances shape flexibility through the oscillating features that come with the use of trigonometric functions. This approach does not only simplify model construction, but helps to improve upon the data fitting capabilities of the new distribution. The proposed secant unit Gompertz (SUG) distribution′s QR framework was attained through the method of reparameterization, where the probability density function (PDF) of the distribution was expressed in terms of its quantile function. The parameters of the distribution were derived using the maximum likelihood estimation procedure under a QR structure and the parameter estimators were shown to be consistent through Monte Carlo simulation analysis. A graphical examination of its PDF revealed that it presents attractive shapes such as skewed, J, reversed J and approximately symmetric, which clearly indicates that the new model can fit data exhibiting these traits. The model was applied to three real datasets to prove its practical usefulness to data from everyday life activities and the results revealed that the proposed SUG QR model consistently offered the best fit through information selection criteria and graphical diagnostics. The results also showed that the proposed model outperformed the unit Chen, unit Gompertz, the unit generalized half normal and the other four contending models in the area of heterogeneity across quantiles and shape flexibility. In conclusion, the study contributes significantly to the current state of knowledge as it has developed a trigonometric extension of the unit Gompertz distribution, broadening its versatility and parsimony in QR modeling involving diverse and intricate data structures.