The beta generalized linear exponential distribution

Mathematica Slovaca

The logarithmic distribution and a given lifetime distribution are compounded to construct a new family of lifetime distributions. The compounding is performed with respect to maxima. Expressions are derived for lifetime properties like moments and the behavior of extreme values. Estimation procedures for the method of maximum likelihood are also derived and their performance assessed by a simulation study. Three real data (including two lifetime data) applications are described that show superior performance (assessed with respect to Kolmogorov Smirnov statistics, likelihood values, AIC values, BIC values, probability-probability plots and density plots) versus at least five known lifetime models, with each model having the same number of parameters as the model it is compared to.

International Journal of Scientific Research in Mathematical and Statistical Sciences

This paper describes the Bayesian inference and prediction of the Exponential Logarithmic distribution. The aim of this paper is to obtain the Bayesian inference of the unknown parameters under different loss functions. The Bayes estimates can be obtained and it has been used to compute the Bayes estimates and also to construct symmetric loss function. We consider the posterior predictive density of the future observations and also asymmetric loss function.

Data Science Journal, 2009

Bayes estimates of the unknown parameter and the reliability function for the generalized exponential model are derived. Bayes estimates are obtained under various losses such as the squared error, the absolute error, the squared log error, and the entropy loss functions. Monte Carlo simulations are presented to compare the Bayes estimates and the maximum likelihood estimates of the unknown parameter and the reliability function.

International Journal of Analysis and Applications, 2020

The exponential distribution is a popular statistical distribution to study the problems in lifetime and reliability theory. We proposed a new generalized exponential distribution, wherein exponentiated exponential and exponentiated generalized exponential distributions are sub-models of the proposed distribution. We study several important statistical and mathematical properties of the newly developed model and provide the simple expressions for the generating function, moments and mean deviations. Parameters of the proposed distribution are estimated by the technique of maximum likelihood. For two real data sets from the field of biology and engineering, the proposed distribution is compared to some existing distributions. It is found that the proposed model is more suitable and useful to study lifetime data. Thus, it gives us another alternative model for existing models.

PLOS ONE, 2020

The paper investigates a new scheme for generating lifetime probability distributions. The scheme is called Exponential-H family of distribution. The paper presents an application of this family by using the Weibull distribution, the new distribution is then called New Flexible Exponential distribution or in short NFE. Various statistical properties are derived, such as quantile function, order statistics, moments, etc. Two real-life data sets and a simulation study have been performed so that to assure the flexibility of the proposed model. It has been declared that the proposed distribution offers nice results than Exponential, Weibull Exponential, and Exponentiated Exponential distribution.

2020

There are several methods to combine and extend the continuous lifetime models to increase their flexibility and generality. Here we proposed a new lifetime distribution model with two parameters. Various lifetime distribution representations related to this model are derived and presented with their properties. Several Statistical measures and their properties are also studied. The method maximum likelihood estimator is discussed. Simulation studies are performed to assess the finite sample performance of the maximum likelihood estimators (MLEs) of the parameters. In the end, to show the flexibility of this distribution, an application using real data sets is presented

The three-parameter gamma and three-parameter Weibull distributions are commonly used for analysing any lifetime data or skewed data. Both distributions have several desirable properties, and nice physical interpretations. Because of the scale and shape parameters, both have quite a bit of flexibility for analysing different types of lifetime data. They have increasing as well as decreasing hazard rate depending on the shape parameter. Unfortunately both distributions also have certain drawbacks. This paper considers a three-parameter distribution which is a particular case of the exponentiated Weibull distribution originally proposed by Mudholkar, Srivastava & Freimer (1995) when the location parameter is not present. The study examines different properties of this model and observes that this family has some interesting features which are quite similar to those of the gamma family and the Weibull family, and certain distinct properties also. It appears this model can be used as an alternative to the gamma model or the Weibull model in many situations. One dataset is provided where the three-parameter generalized exponential distribution fits better than the three-parameter Weibull distribution or the three-parameter gamma distribution.

Biometrics & Biostatistics International Journal

Shanker [2,3] has introduced one parameter continuous distributions named, "Aradhana distribution" and "Sujatha distribution"for modeling lifetime data from engineering and medical science and studied its various mathematical properties, estimation of its parameter, and its applications. A number of continuous distributions for modeling lifetime data have been introduced in statistical literature including exponential, Lindley, gamma, lognormal and Weibull, amongst others. The exponential, Lindley and the Weibull distributions are more popular in practice than the gamma and the lognormal distributions because the survival functions of the gamma and the lognormal distributions cannot be expressed in closed forms and both require numerical integration. Though Aradhana, Sujatha, Lindley and exponential distributions are of one parameter, Aradhana, Sujatha and Lindley distributions have advantage over the exponential distribution that the exponential distribution has constant hazard rate and mean residual life function whereas the Aradhana, Sujatha, and Lindley distributions have increasing hazard rate and decreasing mean residual life function. Further, Aradhana and Sujatha distributions of Shanker [2,3] have flexibility over both Lindley and exponential distributions. Aradhana, Sujatha, Lindley and Exponential Distributions Shanker [2] introduced a new one parameter continuous distribution named, ' Aradhana distribution' for modeling lifetime data from engineering and medical science. This distribution is a three-component mixture of an exponential () θ distribution, a gamma () 2,θ distribution and a gamma () 3,θ distribution with fit than Akash, Shanker, Lindley and exponential distributions in modeling lifetime data. Shanker [2] has discussed its various mathematical and statistical properties including its shape, moment generating function, moments, skewness, kurtosis, hazard rate function, mean residual life function, stochastic orderings, mean deviations, distribution of order statistics, Bonferroni and Lorenz curves, Renyi entropy measure, stress-strength reliability, amongst others. Shanker [4] has also obtained a Poisson mixture Volume 4 Issue 1-2016

arXiv (Cornell University), 2012

We introduce in this paper a new four-parameter generalized version of the linear failure rate (LFR) distribution which is called Beta-linear failure rate (BLFR) distribution. The new distribution is quite flexible and can be used effectively in modeling survival data and reliability problems. It can have a constant, decreasing, increasing, upside-down bathtub (unimodal) and bathtub-shaped failure rate function depending on its parameters. It includes some well-known lifetime distributions as special sub-models. We provide a comprehensive account of the mathematical properties of the new distributions. In particular, A closed-form expressions for the density, cumulative distribution and hazard rate function of the BLFR is given. Also, the rth order moment of this distribution is derived. We discuss maximum likelihood estimation of the unknown parameters of the new model for complete sample and obtain an expression for Fishers information matrix. In the end, to show the flexibility of this distribution and illustrative purposes, an application using a real data set is presented.

In this paper we proposed a new two-parameters lifetime distribution with increasing failure rate. The new distribution arises on a latent complementary risk problem base. The properties of the proposed distribution are discussed, including a formal proof of its probability density function and explicit algebraic formulae for its reliability and failure rate functions, quantiles and moments, including the mean and variance. A simple EM-type algorithm for iteratively computing maximum likelihood estimates is presented. The Fisher information matrix is derived analytically in order to obtaining the asymptotic covariance matrix. The methodology is illustrated on a real data set.