Generalized Linear Failure Rate 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

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.

Quality and Reliability Engineering International, 2020

One of the modern statistical methods is assessing quality performance of product. The performance of a process in the manufacturing and services industry is assessed to examine the level of product quality. The product performance is measured using the lifetime performance index C L , where L is a lower specification limit. In this paper, the maximum likelihood estimation (MLE) of C L for the power Rayleigh distribution is derived based on progressive first-failure-censored sample on the condition of known L is calculated. The hypothesis testing procedure is applied for assessing whether the lifetime of products meets the required level. Finally, real-life data of the number of revolutions before failure of a ball bearing in endurance life time test are used to illustrate the proposed procedure.

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.

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.

Biostatistics and Biometrics Open Access Journal, 2018

In this paper, we proposed a new distribution to lifetime data with two parameters, the proposed distribution have increasing, decreasing and unimodal failure rates function. Some mathematical properties of the new distribution, including hazard function, moments, Estimation of Reliability, distribution of the order statistics and observed information matrix were presented. To estimate the model parameters, the Maximum Likelihood Estimate (MLE) technique was utilized. Then, one real data set were applied to show the significance and flexibility of the new distribution.

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.

Pakistan Journal of Statistics and Operation Research

In this paper we defined a new lifetime model called the the Exponentiated additive Weibull (EAW) distribution. The proposed distribution has a number of well-known lifetime distributions as special submodels, such as the additive Weibull, exponentiated modified Weibull, exponentiated Weibull and generalized linear failure rate distributions among others. We obtain quantile, moments, moment generating functions, incomplete moment, residual life and reversed Failure Rate Functions, mean deviations, Bonferroni and Lorenz curves. The method of maximum likelihood is used for estimating the model parameters. Applications illustrate the potentiality of the proposed distribution.

Communications in Statistics - Simulation and Computation, 2015

We introduce in this paper a new class of distributions which generalizes the linear failure rate (LFR) distribution and is obtained by compounding the LFR distribution and power series (PS) class of distributions. This new class of distributions is called the linear failure rate-power series (LFRPS) distributions and contains some new distributions such as linear failure rate geometric (LFRG) distribution, linear failure rate Poisson (LFRP) distribution, linear failure rate logarithmic (LFRL) distribution, linear failure rate binomial (LFRB) distribution and Raylight-power series (RPS) class of distributions. Some former works such as exponential-power series (EPS) class of distributions, exponential geometric (EG) distribution, exponential Poisson (EP) distribution and exponential logarithmic (EL) distribution are special cases of the new proposed model. The ability of the LFRPS class of distributions is in covering five possible hazard rate function i.e., increasing, decreasing, upside-down bathtub (unimodal), bathtub and increasing-decreasing-increasing shaped. Several properties of the LFRPS distributions such as moments, maximum likelihood estimation procedure via an EM-algorithm and inference for a large sample, are discussed in this paper. In order to show the flexibility and potentiality of the new class of distributions, the fitted results of the new class of distributions and some its submodels are compared using a real data set.

Communications in Statistics - Simulation and Computation

The linear exponential distribution is a generalization of the exponential and Rayleigh distributions. This distribution is one of the best models to fit data with increasing failure rate (IFR). But it does not provide a reasonable fit for modeling data with decreasing failure rate (DFR) and bathtub shaped failure rate (BTFR). To overcome this drawback, we propose a new record-based transmuted generalized linear exponential (RTGLE) distribution by using the technique of Balakrishnan and He (2021). The family of RTGLE distributions is more flexible to fit the data sets with IFR, DFR, and BTFR, and also generalizes several well-known models as well as some new record-based transmuted models. This paper aims to study the statistical properties of RTGLE distribution, like, the shape of the probability density function and hazard function, quantile function and its applications, moments and its generating function, order and record statistics, Rényi entropy. The maximum likelihood estimators, least squares and weighted least squares estimators, Anderson-Darling estimators, Cramér-von Mises estimators of the unknown parameters are constructed and their biases and mean squared errors are reported via Monte Carlo simulation study. Finally, the real data set based on failure time illustrates the goodness of fit and applicability of the proposed distribution; hence, suitable recommendations are forwarded.

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.

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.

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.

Pakistan Journal of Statistics and Operation Research, 2014

We introduce in this paper a new six-parameters generalized version of the generalized linear failure rate (GLFR) distribution which is called McDonald Generalized Linear failure rate (McGLFR) 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, and upside down bathtub-and bathtub shaped failure rate function depending on its parameters. It includes some well-known lifetime distributions as special sub-models. Some structural properties of the new distribution are studied. Expressions for the density, moment generating function, conditional moments, mean deviation, Bonferroni and Lorentz curves also are obtained. Moreover we discuss maximum likelihood estimation of the unknown parameters of the new model.

Statistics & Probability Letters, 2010

Makino Mean hazard rate and its applications to the normal approximation of the Weibull distribution. Naval Research Logistics Quarterly 31, 1-8] proves that, for any random variable X with finite mean µ, E(1/r(X )] 1/µ, where r(•) is the failure rate function of X , with equality if and only if X is exponentially distributed. Here we characterize exponential distribution and Rayleigh distribution through the expected values of r(X ) and e(X ), where e(•) is the mean residual life function of X .