A new lifetime model with decreasing failure rate (original) (raw)
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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.
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Kybernetika, 2014
In this paper, we introduce a general family of continuous lifetime distributions by compounding any continuous distribution and the Poisson-Lindley distribution. It is more flexible than several recently introduced lifetime distributions. The failure rate functions of our family can be increasing, decreasing, bathtub shaped and unimodal shaped. Several properties of this family are investigated including shape characteristics of the probability density, moments, order statistics, (reversed) residual lifetime moments, conditional moments and Rényi entropy. The parameters are estimated by the maximum likelihood method and the Fisher's information matrix is determined. Several special cases of this family are studied in some detail. An application to a real data set illustrates the performance of the family of distributions.
A lifetime model with increasing failure rate
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This paper deals with a new two-parameter lifetime distribution with increasing failure rate. This distribution is constructed as a distribution of a random sum of independent exponential random variables when the sample size has a zero truncated binomial distribution. Various statistical properties of the distribution are derived. We estimate the parameters by maximum likelihood and obtain the Fisher information matrix. Simulation studies show the performance of the estimators. Also, estimation of the parameters is considered in the presence of censoring. A real data set is analyzed for illustrative purposes and it is noted that the distribution is a good competitor to the gamma, Weibull, exponentiated exponential, weighted exponential and Poisson-exponential distributions for this data set.
A lifetime distribution with decreasing failure rate
Statistics & Probability Letters, 1998
A two-parameter distribution with decreasing failure rate is introduced. Various properties are discussed and the estimation of parameters is studied by the method of maximum likelihood. The estimates are attained by the EM algorithm and expressions for their asymptotic variances and covariances are obtained. Numerical examples based on real data are presented. ~)
A novel family of lifetime distribution with applications to real and simulated data
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.
Computational Statistics & Data Analysis, 2007
A new two-parameter distribution with decreasing failure rate is introduced. Various properties of the introduced distribution are discussed. The EM algorithm is used to determine the maximum likelihood estimates and the asymptotic variances and covariance of these estimates are obtained. Simulation studies are performed in order to assess the accuracy of the approximation of the variances and covariance of the maximum likelihood estimates and investigate the convergence of the proposed EM scheme. Illustrative examples based on real data are also given.
On Some One Parameter Lifetime Distributions and their Applications
Annals of Biostatistics & Biometric Applications
The time to the occurrence of event of interest is known as lifetime or survival time or failure time in reliability analysis. The event may be failure of a piece of equipment, death of a person, development (or remission) of symptoms of disease, health code violation (or compliance). The modeling and statistical analysis of lifetime data are crucial for statisticians and research workers in almost all applied sciences including engineering, medical science/ biological science, insurance and finance, amongst others. The classical lifetime distribution namely exponential distribution and Lindley distribution introduced by Lindley (1958) distribution are popular in statistics for modeling lifetime data. But these two classical lifetime distributions are not suitable from theoretical and applied point of view. Shanker et al (2015) have done a critical and comparative study regarding the modeling of lifetime data using both exponential and Lindley distributions and found that there are several lifetime data where these classical lifetime distributions are not suitable due to their shapes, hazard rate functions and mean residual life functions, amongst others. Recently, a number of one parameter lifetime distributions have been introduced by Shanker, namely Shanker,
A New Compound Gamma and Lindley Distribution with Application to Failure Data
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.
A new family of compound exponentiated logarithmic distributions with applications to lifetime data
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.
The exponentiated Lomax Poisson distribution with an application to lifetime data
2013
Generalizing lifetime distributions is always precious for applied statisticians. By compounding the exponentiated Lomax and Poisson distributions, a new continuous distribution is introduced, called the exponentiated Lomax Poisson distribution. The new model extends the Lomax distribution and some other distributions and it is quite flexible to analyze positive data. Various structural properties of the new distribution are derived including explicit expressions for the ordinary and incomplete moments, generating and quantile functions, mean deviations, Lorenz and Bonferroni curves, reliability, Rényi and Manoel Wallace A. Ramos et al. 108 Shannon entropies, order statistics and their moments. The estimation of the model parameters is performed by maximum likelihood. We also determine the observed information matrix. The potentiality of the new model is illustrated by means of a real data set. We hope that the new distribution will serve as an alternative model to other distributions available in the literature for modeling lifetime real data in many areas.