Ibrahim Abdullahi

Cure fraction models provide a useful framework for analysing survival data in which some individuals may never experience the event of interest. This paper introduces a flexible Nakagami–Weibull Non-Mixture Cure (NWNMC) model for right-censored survival data with a long-term surviving fraction, constructed by embedding the Nakagami–Weibull baseline distribution within the promotion-time cure framework. This provides additional flexibility for capturing complex survival and hazard rate behaviours. Several key mathematical properties of the model are established, and parameter estimation is carried out using maximum likelihood under right censoring, with inferential procedures developed based on the observed information matrix. A Monte Carlo simulation study examines the finite-sample performance of the maximum likelihood estimators under different parameter values and sample sizes, showing that the estimators are reliable, with decreasing bias and root mean square error as the sample size increases. The practical usefulness of the proposed model is demonstrated through two real-data applications involving business customer churn and colon cancer survival data. The NWNMC model provides the best fit for the customer churn data and remains competitive for the colon cancer data. These results confirm that the proposed model offers a flexible and effective alternative for modelling heterogeneous survival data with a cure fraction.

This article proposes a new distribution called the mixture Nakagami-Rayleigh (mNR) distribution, which is obtained by combining Nakagami and Rayleigh distributions. The maximum likelihood estimator (MLE) is the primary approach we propose to estimate the parameters for the mN-R distribution. This paper also presents related functions of the mNR distribution, such as the survival function, the probability density function (PDF), the cumulative distribution function (CDF), and the hazard function, along with the important mathematical properties of the mNR distribution. Additionally, plots of the important functions of the mNR distribution are illustrated as line plots and contour plots. Furthermore, we present a simulation study to demonstrate the flexibility of the mNR distribution. Finally, the article concludes by summarizing the key outcomes and providing recommendations for future work.

This article proposes the new Nakagami-generated family of distribution (NNak-G) and the new Nakagami-Exponential (NNak-E) distribution for fitting skewed and heavy-tailed data. By integrating the flexibility of the Nakagami distribution with the useful properties of the exponential distribution, the NNak-E distribution provides enhanced adaptability for fitting with right-skewed data structures. The theoretical properties of the NNak-E distribution are developed, including its distribution function, density function, moments, and hazard function. Parameter estimation is constructed using the Maximum Likelihood Estimation (MLE) method, and a comprehensive simulation study is performed to evaluate the performance of the MLE estimates. Furthermore, the NNak-E distribution is applied to real-world datasets, where it demonstrates superior goodness-of-fit compared to existing distributions. The results confirm that NNak-E is a choice distribution for practitioners and researchers dealing with asymmetric and heavy-tailed data distributions in diverse fields such as engineering, medical research, and risk assessment.

This paper provides a Bayesian framework for estimating parameters of the length-biased Nakagami (LBN) distribution. We derive the maximum likelihood estimator (MLE) and Bayesian estimators under three different loss functions: the squared error loss function, the quadratic loss function, and the precautionary loss function. A simulation study is conducted to compare the performance of three different loss functions and the MLE with a fixed shape parameter. Moreover, a real data application illustrates the performance of these estimators.

This article introduces a new mixture extension of the Maxwell–Boltzmann distribution (MBD) to enhance data modeling flexibility. Maximum Likelihood Estimation (MLE) is employed to estimate parameters, and key statistical properties are analyzed. In addition, simulation studies are conducted to compare the bias, mean square error, and variance of the estimates over a wide range of sample sizes from n = 5 to 10,000. The new distribution is applied to a real-world heart attack survival dataset to demonstrate its potential in practical applications. These findings highlight the potential of the proposed distribution in survival studies and modeling right-skewed data.

In the past few decades, numerous efforts have been made to develop a new class of lifetime distributions with greater flexibility by extending known distributions. In this paper, the two popular distributions, Nakagami and Rayleigh, were selected and combined to create a new distribution, namely the Nakagami–Rayleigh (NK-R) distribution, to obtain a distribution that was better than each other. First, its probability density and cumulative function expressions were initially derived. Then, some distributional properties such as survival function, hazard function, moment generating function, and order statistics were investigated. Next, the parameters were estimated by the maximum likelihood method, and their performance was evaluated via a simulation study with varying parameter values and sample sizes. Finally, the proposed distribution has been fitted to a real-life data set to examine its potential and flexibility. The results indicated that the offered estimators performed nicely. Furthermore, based on the Akaike information criterion, the proposed distribution provided a more appropriate model than other candidate distributions in terms of goodness of fit.

In recent decades, there have been numerous endeavors to develop a novel category of survival distributions possessing enhanced flexibility through the extension of existing distributions. This article constructs and validates the statistical properties of a novel survival distribution in order to obtain an alternative distribution that is suitable for analyzing survival data by presenting the novel mixture of the Fréchet distribution along with statistical properties such as the probability density function (PDF), cumulative distribution function (CDF), rth ordinary moment, skewness, kurtosis, moment-generating function, mean, variance, mode, survival function, hazard function, and asymptotic behavior, as well as constructing the estimators of the unknown parameter by employing the expectation-maximization (EM) algorithm, and simulated annealing. Additionally, the performance of the proposed estimators was compared with bias, mean squared errors (MSE), and simulated variances, and given an illustrative example of the proposed distribution to the survival data set in order to show that the proposed distribution is appropriate for the right-skewed data. This will be extremely advantageous in survival analysis.