Generalized Lindley Distribution Research Articles

Estimation and prediction for Type-I hybrid censored data from generalized Lindley distribution

This paper consider the problems of estimation and prediction using Type-I hybrid censored lifetime data that follow generalized Lindley distribution. Maximum likelihood estimators as well as Bayes estimators have been proposed for estimating the parameters and reliability characteristics from the generalized Lindley distribution. Since posteriors are not in closed forms, Markov Chain Monte Carlo techniques such as Gibbs sampler and Metropolis-Hastings algorithm have been utilized to explore the properties of the posteriors. Monte Carlo simulation study has been carried out to compare the classical and Bayesian estimation methods. One and two sample predictive posteriors of future order statistics are also derived on the basis of Type-I hybrid censored data. Finally, a set of real data is analysed for illustration.

English

English

Parameter Estimation and Joint Confidence Regions for the Parameters of the Generalized Lindley Distribution

We deal with the problem of estimating the parameters of the generalized Lindley distribution. Besides the classical estimator, inverse moment and modified inverse estimators are proposed and their properties are investigated. A condition for the existence and uniqueness of the inverse moment and modified inverse estimators of the parameters is established. Monte Carlo simulations are conducted to compare the estimators’ performances. Two methods for constructing joint confidence regions for the two parameters are also proposed and their performances are discussed. A real example is presented to illustrate the proposed methods.

A Comparison of Size and Power of Tests of Hypotheses on Parameters Based on Two Generalized Lindley Distributions

This study compares two generalized Lindley distributions and assesses consistency between theoretical and analytical results. Data (complete and censored) assumed to follow the Lindley distribution are generated and analyzed using two generalized Lindley distributions, and maximum likelihood estimates of parameters from the generalized distributions are obtained. Size and power of tests of hypotheses on the parameters are assessed drawing on asymptotic properties of the maximum likelihood estimates. Results suggest that whereas size of some of the tests of hypotheses based on the considered generalized distributions are essentially α-level, some are possibly not; power of tests of hypotheses on the Lindley distribution parameter from the two distributions differs.

An Extended Generalized Lindley Distribution and Its Applications to Lifetime Data

An Extended Generalized Lindley Distribution and Its Applications to Lifetime Data

Exponentiated power Lindley distribution

A new generalization of the Lindley distribution is recently proposed by Ghitany et al. [1], called as the power Lindley distribution. Another generalization of the Lindley distribution was introduced by Nadarajah et al. [2], named as the generalized Lindley distribution. This paper proposes a more generalization of the Lindley distribution which generalizes the two. We refer to this new generalization as the exponentiated power Lindley distribution. The new distribution is important since it contains as special sub-models some widely well-known distributions in addition to the above two models, such as the Lindley distribution among many others. It also provides more flexibility to analyze complex real data sets. We study some statistical properties for the new distribution. We discuss maximum likelihood estimation of the distribution parameters. Least square estimation is used to evaluate the parameters. Three algorithms are proposed for generating random data from the proposed distribution. An application of the model to a real data set is analyzed using the new distribution, which shows that the exponentiated power Lindley distribution can be used quite effectively in analyzing real lifetime data.

A new class of generalized Lindley distributions with applications

A new four-parameter class of generalized Lindley (GL) distribution called the beta-generalized Lindley (BGL) distribution is proposed. This class of distributions contains the beta-Lindley, GL and Lindley distributions as special cases. Expansion of the density of the BGL distribution is obtained. The properties of these distributions, including hazard function, reverse hazard function, monotonicity property, shapes, moments, reliability, mean deviations, Bonferroni and Lorenz curves are derived. Measures of uncertainty such as Renyi entropy and s-entropy as well as Fisher information are presented. Method of maximum likelihood is used to estimate the parameters of the BGL and related distributions. Finally, real data examples are discussed to illustrate the applicability of this class of models.

Estimation on System Reliability in Generalized Lindley Stress-Strength Model

This paper discusses the problem of the estimation of stressed system reliability under both classical and Bayesian paradigms. It is assumed that the strength of a system and the environmental stress applied on it, follow the generalized Lindley distribution. For Bayesian calculation, we proposed the use of MCMC technique viz Metropolis-Hastings algorithm to approximate the posteriors of the stress-strength parameters. The behaviours of th e maximum likelihood and Bayes estimators of stress-strength parameters and reliability have been studied through the Monte Carlo simulation study. Finally, the empirical illustration based on a real data set has been provided.

The Log–Lindley distribution as an alternative to the beta regression model with applications in insurance

In this paper a new probability density function with bounded domain is presented. The new distribution arises from the generalized Lindley distribution proposed by Zakerzadeh and Dolati (2010). This new distribution that depends on two parameters can be considered as an alternative to the classical beta distribution. It presents the advantage of not including any special function in its formulation. After studying its most important properties, some useful results regarding insurance and inventory management applications are obtained. In particular, in insurance, we suggest a special class of distorted premium principles based on this distribution and we compare it with the well-known power dual premium principle. Since the mean of the new distribution can be normalized to give a simple parameter, this new model is appropriate to be used as a regression model when the response is bounded, being therefore an alternative to the beta regression model recently proposed in the statistical literature.

Expected total test time and Bayesian estimation for generalized Lindley distribution under progressively Type-II censored sample where removals follow the Beta-binomial probability law

In this paper, we have proposed the progressive Type-II censoring scheme which allows the removals of the live units from a life-test with Beta-binomial probability law during the execution of the experiment. To stablish the theory, the generalized Lindley distribution is considered. For our proposed procedure, the behaviour of the expected total test time has been investigated through the numerical study. The classical as well as the Bayesian procedures for the estimation of the unknown model parameters have also been developed under this censoring scheme. Further, the discussion has been extended to the prediction of the future samples under Bayesian paradigm. Finally, a real data set has been analysed to illustrate the discussed methodology.

Weighted Dagum and related distributions

In this paper, a new class of weighted Dagum and related distributions is proposed. Probability weighted moments of Dagum distribution and the resulting weighted distributions are presented. This class of distributions contains several weighted Dagum distributions such as length-biased Dagum, proportional hazard moment Dagum, proportional reverse hazard moment Dagum and Dagum distributions as special cases. Entropy and Fisher information of the weighted Dagum distribution are derived. We estimates the model parameters via the maximum likelihood estimation procedure. Examples and comparison of this model with the weighted generalized gamma, generalized gamma and generalized Lindley distributions are presented.

A generalized Lindley distribution

A new distribution is proposed for modeling lifetime data. It has better hazard rate properties than the gamma, lognormal and the Weibull distributions. A comprehensive account of the mathematical properties of the new distribution including estimation and simulation issues is presented. A real data example is discussed to illustrate its applicability.

Generalized Poisson–Lindley Distribution

An extended version of the compound Poisson distribution is obtained by compounding the Poisson distribution with the generalized Lindley distribution. Estimation of the parameters is discussed using the method of moments and maximum likelihood estimators. Examples are given of the fitting of this distribution to data, and the fit is compared with that obtained using other distributions.