A New Distribution with two parameters to Lifetime Data

2011

In this paper we introduce a new lifetime distribution by compounding exponential and Poisson-Lindley distributions, named exponential Poisson-Lindley distribution. Several properties are derived, such as density, failure rate, mean lifetime, moments, order statistics and Rényi entropy. Furthermore, estimation by maximum likelihood and inference for large sample are discussed. The paper is motivated by two applications to real data sets and we hope that this model be able to attract wider applicability in survival and reliability.

In this paper, we introduce a new extension of the generalized linear failure rate distributions. It includes some well-known lifetime distributions such as extension of generalized exponential and generalized linear failure rate distributions as special sub-models. In addition, it can have a constant, decreasing, increasing, upside-down bathtub (unimodal), and bathtub-shaped hazard rate function depending on its parameters. We provide some of its statistical properties such as moments, quantiles, skewness, kurtosis, hazard rate function, and reversible hazard rate function. The maximum likelihood estimation of the parameters is also discussed. At the end, a real data set is given to illustrate the usefulness of this new distribution in analyzing lifetime

Computational Statistics & Data Analysis, 2008

A four parameter generalization of the Weibull distribution capable of modeling a bathtubshaped hazard rate function is defined and studied. The beauty and importance of this distribution lies in its ability to model monotone as well as non-monotone failure rates, which are quite common in lifetime problems and reliability. The new distribution has a number of well-known lifetime special sub-models, such as the Weibull, extreme value, exponentiated Weibull, generalized Rayleigh and modified Weibull distributions, among others. We derive two infinite sum representations for its moments. The density of the order statistics is obtained. The method of maximum likelihood is used for estimating the model parameters. Also, the observed information matrix is obtained. Two applications are presented to illustrate the proposed distribution.

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.

Biometrics & Biostatistics International Journal, 2019

In this paper, a comparative study on some selected one parameter distributions has been carried out. The important properties of distributions have been compared using various datasets from engineering, biological sciences and other fields. The lifetime data have been taken from various fields of studies. Various proposed models have been applied on data to check goodness of fit and their behavior have been discussed with graphically.

In this paper, we introduce a new lifetime distribution. Characteristics and statistical properties are obtained, such as stress strength reliability, moments, entropy, and order statistics. Moreover, the estimation of the parameter of the proposed distribution for the complete sample are discussed using different estimation methods like percentiles, least squares estimation, weighted least squares estimation, maximum likelihood estimation, and Cramer-von-mises estimations and compared them using Monte Carlo simulation study. The model parameter is obtained under hybrid censoring based on the censored sample. The actuarial measures are calculated for our model and the result is compared with the risk of the exponential distribution. Finally, an application of two real data sets is used to illustrate the proposed model.

International Journal of Computational and Theoretical Statistics, 2018

This paper derives a new four-parameter generalized exponential power lifetime probability model for life time data, which generalizes some well-known exponential power lifetime distributions. It is observed that our proposed new distribution bears most of the properties of skewed distributions in reliability and life testing context. It is skewed to the right as well as its failure rate function has the increasing and bathtub shape behaviors. The estimation of the parameters, and simulation and applications of the proposed model have also been discussed.

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.

FUDMA JOURNAL OF SCIENCES, 2020

A lifetime model called Transmuted Exponential-Weibull Distribution was proposed in this research. Several statistical properties were derived and presented in an explicit form. Maximum likelihood technique is employed for the estimation of model parameters, and a simulation study was performed to examine the behavior of various estimates under different sample sizes and initial parameter values. Through using real-life datasets, it was empirically shown that the new model provides sufficient fits relative to other existing models.

Austrian Journal of Statistics

In this paper, we propose a new lifetime distribution by compounding the gamma and Lindley distributions. Construction of it can be interpreted in the viewpoint of the reliability analysis and Bayesian inference. Moreover, the distribution has decreasing and unimodal hazard rate shapes. Several properties of the distribution are obtained, involving characteristics of the (reverse) hazard rate function, quantiles, moments, extreme order statistics and some stochastic order relations. Estimating the distribution parameters is discussed by some estimation methods and their performance is evaluated by a simulation study. Also, estimation of the stress-strength parameter is investigated. Usefulness of the distribution among other models is illustrated by fitting two failure data sets and using some goodness-of-fit measures.