• Communications for Statistical Applications and Methods
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• v.23 no.6
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• pp.517-529
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• 2016

This study compares the inverse transform and the composition methods for generating data from the Lindley distribution. The expression for the inverse of the distribution function for the Lindley distribution does not exist in closed form. Hence, authors of many empirical studies on the Lindley distribution used methods for generating Lindley variates other than the inverse transform. We generated data from the Lindley distribution using the inverse transform approach by obtaining the Lindley variates numerically; we also generated data from this distribution using the composition approach. Following the generation of the Lindley variates using these two methods, we compare some statistical properties of the estimates of the Lindley model parameters based on the generated data. We conclude that the two methods produce similar results.

• Communications for Statistical Applications and Methods
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• v.24 no.3
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• pp.193-209
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• 2017

The power Lindley distribution with some of its properties is considered in this article. Maximum likelihood, least squares, maximum product spacings, and Bayes estimators are proposed to estimate all the unknown parameters of the power Lindley distribution. Lindley's approximation and Markov chain Monte Carlo techniques are utilized for Bayesian calculations since posterior distribution cannot be reduced to standard distribution. The performances of the proposed estimators are compared based on simulated samples. The waiting times of research articles to be accepted in statistical journals are fitted to the power Lindley distribution with other competing distributions. Chi-square statistic, Kolmogorov-Smirnov statistic, Akaike information criterion and Bayesian information criterion are used to access goodness-of-fit. It was found that the power Lindley distribution gives a better fit for the data than other distributions.

• Communications for Statistical Applications and Methods
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• v.22 no.3
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• pp.233-239
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• 2015

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 ${\alpha}$-level, some are possibly not; power of tests of hypotheses on the Lindley distribution parameter from the two distributions differs.

• Communications for Statistical Applications and Methods
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• v.18 no.4
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• pp.485-493
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• 2011

The proportional likelihood ratio order is an extension of the likelihood ratio order for the non-negative absolutely continuous random variables. In addition, the Lindley distribution has been over looked as a mixture of two exponential distributions due to the popularity of the exponential distribution. In this paper, we first recalled the above concepts and then obtained various properties of the Lindley distribution due to the proportional likelihood ratio order. These results are more general than the likelihood ratio ordering aspects related to this distribution. Finally, we discussed the proportional likelihood ratio ordering in view of the weighted version of the Lindley distribution.

• Communications for Statistical Applications and Methods
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• v.24 no.2
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• pp.129-142
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• 2017

In this paper we consider the problem of the model selection/discrimination among three different positively skewed lifetime distributions. Lindley, Weibull, and gamma distributions have been used to effectively analyze positively skewed lifetime data. This paper assesses how much closer the Lindley distribution gets to Weibull and gamma distributions. We consider three techniques that involve the likelihood ratio test, asymptotic likelihood ratio test, and minimum Kolmogorov distance as optimality criteria to diagnose the appropriate fitting model among the three distributions for a given data set. Monte Carlo simulation study is performed for computing the probability of correct selection based on the considered optimality criteria among these families of distributions for various choices of sample sizes and shape parameters. It is observed that overall, the Lindley distribution is closer to Weibull distribution in the sense of likelihood ratio and Kolmogorov criteria. A real data set is presented and analyzed for illustrative purposes.

• International Journal of Reliability and Applications
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• v.17 no.1
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• pp.1-19
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• 2016

The Exponentiated Quasi Lindley (EQL) distribution which is an extension of the quasi Lindley Distribution is introduced and its properties are explored. This new distribution represents a more flexible model for the lifetime data. Some statistical properties of the proposed distribution including the shapes of the density and hazard rate functions, the moments and moment generating function, the distribution of the order statistics are given. The maximum likelihood estimation technique is used to estimate the model parameters and finally an application of the model with a real data set is presented for the illustration of the usefulness of the proposed distribution.

• Honam Mathematical Journal
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• v.25 no.1
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• pp.95-115
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• 2003

Consider the problem of estimating a $p{\times}1$ mean vector ${\theta}(p{\geq}4)$ under the quadratic loss, based on a sample $X_1,\;{\cdots}X_n$. We find an optimal decision rule within the class of Lindley type decision rules which shrink the usual one toward the mean of observations when the underlying distribution is that of a variance mixture of normals and when the norm $||{\theta}-{\bar{\theta}}1||$ is known, where ${\bar{\theta}}=(1/p)\sum_{i=1}^p{\theta}_i$ and 1 is the column vector of ones. When the norm is restricted to a known interval, typically no optimal Lindley type rule exists but we characterize a minimal complete class within the class of Lindley type decision rules. We also characterize the subclass of Lindley type decision rules that dominate the sample mean.

• Nonlinear Functional Analysis and Applications
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• v.28 no.3
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• pp.793-800
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• 2023

In this paper, we propose a generalization of Lindley distribution (GLD) via a special structure that is concern with progressively Type-II right censoring and time failure data. We study the modern properties that we have built by such combination, for example, survival function, hazard function, moments, and estimation by non-Bayesian methods. Application on some selected data related to Lindley distribution (LD) and (ED) have been employed to find out the best distribution that can fit data comparing with the GLD.

• Journal of the Korean Data and Information Science Society
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• v.22 no.6
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• pp.1251-1256
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• 2011

Consider a p-variate ($p{\geq}4$) normal distribution with mean ${\theta}$ and identity covariance matrix. Using a simple property of noncentral chi square distribution, the generalized Bayes estimators dominating the Lindley estimator under quadratic loss are given based on the methods of Brown, Brewster and Zidek for estimating a normal variance. This result can be extended the cases where covariance matrix is completely unknown or ${\Sigma}={\sigma}^2I$ for an unknown scalar ${\sigma}^2$.

• Journal of the Korean Data and Information Science Society
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• v.16 no.4
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• pp.1027-1039
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• 2005

Consider the problem of estimating a $p{\times}1$ mean vector $\theta(p\geq4)$ under the quadratic loss, based on a sample $X_1$, $X_2$, $\cdots$, $X_n$. We find a Lindley type decision rule which shrinks the usual one toward the mean of observations when the underlying distribution is that of a variance mixture of normals and when the norm $\parallel\;{\theta}-\bar{{\theta}}1\;{\parallel}$ is restricted to a known interval, where $bar{{\theta}}=\frac{1}{p}\;\sum\limits_{i=1}^{p}{\theta}_i$ and 1 is the column vector of ones. In this case, we characterize a minimal complete class within the class of Lindley type decision rules. We also characterize the subclass of Lindley type decision rules that dominate the sample mean.