Joseph Thomas Eghwerido

This article examined some of the characteristics of the New Sine Inverse Rayleigh Distribution. There is just one scale parameter in the New Sine Inverse Rayleigh distribution. The raw moments, reliability analysis, and other aspects of the New Sine Inverse Rayleigh Distribution have been derived. The maximum likelihood approach was used to estimate the New Sine Inverse Rayleigh Distribution’s parameters. Utilizing simulation, the distribution’s stability was examined, and the applicability of the distribution was demonstrated using three data sets. The analysis’s findings demonstrated that the New Sine Inverse Rayleigh Distribution behaves well and fits the data more closely than other probability distributions.

The generalization of the family of distributions that could provide a simple, and efficient algorithm for parameter estimation and study of the behavior of datasets from various fields has received significant interest. Such a model has enormous advantages, such as its flexible nature, and the regression form can easily be derived. In the literature, various generalized families of distributions have been introduced. Despite the merits of these distributions, they still have some limitations due to many parameters in the model. Thus, the estimation of parameters often becomes cumbersome. Therefore, this study introduced the alpha power Muth or Teissier-G family of continuous distributions with well-defined parameters, and obtained the joint progressive type-II censoring scheme and their reliability measures. Furthermore, we obtained the global and local influences of the APTG model. We used real-life and simulated data to evaluate the numerical applications of the introduced model. The results show that the alpha power Muth or Teissier-G family of distributions gave the best fits to both datasets than some existing models.

This article is set to push new boundaries with leading-edge innovations in statistical distribution for generating up-to-the-minute contemporary distributions by a mixture of the second record value of the Gompertz distribution and the classical Gompertz model (weighted Gompertz model) using T-X characterization, especially used for two-sided schemes that provide an accurate model. The quantile, ordinary, and complete moments, order statistics, probability, and moments generating functions, entropies, probability weighted moments, Lin’s condition random variable, reliability in multicomponent stress strength system, reversed, and moments of residuals life and other reliability characteristics in engineering, actuarial, economics, and environmental technology were derived in their closed form. To investigate and test the flexibility, viability, tractability, and performance of the proposed Weighted Gompertz-G (WGG) generated model, the shapes of some sub-models of the WGG model were examined. The shapes of the sub-models indicated J-shapes, increasing, decreasing, and bathtub hazard rate functions. The maximum likelihood estimation of the WGG-generated model parameters was examined. An illustration with simulation and real-life data analysis indicated that the WGG-generated model provides consistently better goodness-of-fit statistics than some competitive models in the literature.

This study introduces a parsimonious and tractable generator for continuous distribution called the Teissier-G family of distributions for continuous random variables and examines the distributions belonging to this family as the sub-models. Some general statistical characteristics and sub-models of the new generator were examined and studied. Similarly, we examined the shapes of the sub-models probability density function (pdf) and hazard rate function were investigated. The parameter of the proposed model was obtained in a closed form by maximum likelihood. In addition to the numerical real life applications, Monte Carlo simulation was performed to examine the flexibility of the introduced models. The models provide good fits in all the cases. The results show great improvement compared to existing models.

This paper introduces a two-parameters generator of continuous statistical probability distributions called the Alpha Power Rayleigh-G (APRAY-G) family, some statistical properties of the family of distributions were derived, and we introduced a two-submodels of the generator. We estimate the parameters of the models based on the method of maximum likelihood estimation and explored simulation studies based on the introduced submodels. We observed that the biasedness and root mean square errors decrease as the sample size becomes large. We examined the applications of the models based on real-life data sets. We compared the obtained results with some existing probability distribution models. The results showed that the proposed models gave a better fitness to the data under investigation.

This article introduced the determination of reliability analysis of the alpha power Gompertz model using the Bayesian techniques. The method developed has been evaluated using women breast cancer in the Stan implementation in R. A survival data used illustrates the proposed Bayesian approach.

This article proposes the alpha power extended generalized exponential distribution. This distribution is a unique case of the alpha power family of distribution with a generalization of the exponential distribution. The statistical properties of the proposed distribution such as survival function hazard function cumulative distribution function moment generating function, kurtosis, skewness, order statistics, odd function, cumulative function, reversed hazard, entropy and quantile are established. The parameters estimate of the proposed distribution were obtained by maximum likelihood method. The flexibility of the propose distribution was examined using two real life datasets. The goodness of fit of the proposed model indicates that the new distribution performed better than some existing distributions.