A New Family of Continuous Distributions: Properties and Estimation

A NEW flexible exponent power family of distributions with biomedical data analysis

Probability distributions are widely utilized in applied sciences, especially in the field of biomedical science. Biomedical data typically exhibit positive skewness, necessitating the use of flexible, skewed distributions to effectively model such phenomena. In this study, we introduce a novel approach to characterize new lifetime distributions, known as the New Flexible Exponent Power (NFEP) Family of distributions. This involves the addition of a new parameter to existing distributions. A specific sub-model within the proposed class, known as the New Flexible Exponent Power Weibull (NFEP-Wei), is derived to illustrate the concept of flexibility. We employ the well-established Maximum Likelihood Estimation (MLE) method to estimate the unknown parameters in this family of distributions. A simulation study is conducted to assess the behavior of the estimators in various scenarios. To gauge the flexibility and effectiveness of the NFEP-Wei distribution, we compare it with the AP-Wei (alpha power Weibull), MO-Wei (Marshal Olkin Weibull), classical Wei (Weibull), NEP-Wei (new exponent power Weibull), FRLog-Wei (flexible reduced logarithmic Weibull), and Kum-Wei (Kumaraswamy Weibull) distributions by analyzing four distinct biomedical datasets. The results demonstrate that the NFEP-Wei distribution outperforms the compared distributions.

Classical and Bayesian Inference on Finite Mixture of Exponentiated Kumaraswamy Gompertz and Exponentiated Kumaraswamy Fréchet Distributions under Progressive Type II Censoring with Applications

A finite mixture of exponentiated Kumaraswamy Gompertz and exponentiated Kumaraswamy Fréchet is developed and discussed as a novel probability model. We study some useful structural properties of the proposed model. To estimate the model parameters under the classical method, we use the maximum likelihood estimation using a progressive type II censoring scheme. Under the Bayesian paradigm the estimation is carried out with gamma priors under a progressive type II censored samples with squared error loss function. To demonstrate the efficiency of the proposed model based on progressively type II censoring, a simulation study is carried out. Three actual data sets are used as an example, demonstrating that the suggested model in the new class fits better than the existing finite mixture models available in the literature.

The Generalized Alpha Exponent Power Family of Distributions: Properties and Applications

Here, a new method is recommended to characterize a new continuous distribution class, named the generalized alpha exponent power family of distributions (GAEPFDs). A particular sub-model is presented for exemplifying the objective. The basic statistical properties, such as ordinary moments, the probability weighted moments, mode, quantile, order statistics, entropy measures, and moment generating functions, etc., were explored. To gauge the GAEPPRD parameters, the ML technique was utilized. The estimator behaviour was studied by a Monte Carlo simulation study (MCSS). The effectiveness of GAEPFDs was demonstrated observationally through lifetime data. The applications show that GAEPFDs can offer preferable results over other competitive models.

A Modified Power Family of Distributions: Properties, Simulations and Applications

In this paper, we present a new class of distributions called the modified power family by adding an extra shape parameter. Some of its structural properties are derived. Three special cases of the new family are considered and estimated using the method of maximum likelihood. The validity of the method of maximum likelihood is illustrated via Monte Carlo simulations. The importance and flexibility of the new family are empirically illustrated, partly due to efficient modeling of several real data. We compare the proposed family with some distributions and special models generated from other classes using classical statistical measures.