Generalized Lindley Distribution Research Articles

Bivariate Poisson Generalized Lindley Distributions and the Associated BINAR(1) Processes

This paper proposes new bivariate distributions based on the Poisson generalized Lindley distribution as marginal. These models include the basic bivariate Poisson generalized Lindley (BPGL) and the Sarmanov-based bivariate Poisson generalized Lindley (SPGL) distributions. Subsequently, we introduce the BPGL and SPGL distributions as joint innovation distributions in a novel bivariate first-order integer-valued autoregressive process (BINAR(1)) based on binomial thinning. The model parameters in the BPGL and SPGL distributions are estimated using the method of maximum likelihood (ML) while we apply the conditional maximum likelihood (CML) for the BINAR(1) process. We conduct some simulation experiments to assess the small and large sample performances. Further, we implement the new BINAR(1)s to the Pittsburgh crime series data and they show better fitting criteria than other competing BINAR(1) models in the literature.

A New Poisson Generalized Lindley Regression Model

In this paper, a new count distribution is introduced. It is a mixture of the Poisson and generalized Lindley distributions. Statistical properties of the proposed distribution including the factorial moments, probability generating function, moment generating function and moments are studies. Maximum likelihood estimators of unknown parameters are derived. Moreover, an alternative count regression model based on the proposed distribution is presented. Finally, the proposed model is applied for real data and compared with other well-known models.

Inference for constant stress accelerated life test under the proportional reverse hazards lifetime distribution

AbstractIn this paper, we consider small sample statistical inference methods for the constant stress accelerated life test (CSALT) under the proportional reverse hazards family (PRHF). The model parameters are assumed to be the exponential functions of the stress. The generalized confidence intervals (GCIs) are derived for the model parameters and some commonly used reliability metrics such as the quantile and the reliability function of the lifetime at the designed stress level. The generalized prediction interval (GPI) is also proposed for the future failure time (FFT) and the remaining useful life (RUL) at the designed stress level. The Monte Carlo simulation study for the generalized Lindley distribution (GLD) and the inverse Weibull distribution are used to illustrate the performance of the proposed GCIs and GPI. The simulation results indicate that the performance of the proposed GCIs and GPI is better than the Wald confidence intervals (CIs) and bootstrap‐p CIs in terms of the coverage probability (CP). Finally, a real example is used to illustrate the developed procedures.

A New Generalized Lindley Distribution

In this paper, we present a new class of distributions called New Generalized Lindley Distribution(NGLD). This class of distributions contains several distributions such as gamma, exponential and Lindley as special cases. The hazard function, reverse hazard function, moments and moment generating function and inequality measures are are obtained. Moreover, we discuss the maximum likelihood estimation of this distribution. The usefulness of the new model is illustrated by means of two real data sets. We hope that the new distribution proposed here will serve as an alternative model to other models available in the literature for modelling positive real data in many areas.

The Negative Binomial-New Generalized Lindley Distribution for Count Data: Properties and Application

In this paper, a new mixture distribution for count data, namely the negative binomial-new generalized Lindley (NB-NGL) distribution is proposed. The NB-NGL distribution has four parameters, and is a flexible alternative for analyzing count data, especially when there is over-dispersion in the data. The proposed distribution has sub-models such as the negative binomial-Lindley (NB-L), negative binomial-gamma (NB-G), and negative binomial-exponential (NB-E) distributions as the special cases. Some properties of the proposed distribution are derived, i.e., the moments and order statistics density function. The unknown parameters of the NB-NGL distribution are estimated by using the maximum likelihood estimation. The results of the simulation study show that the maximum likelihood estimators give the parameter estimates close to the parameter when the sample is large. Application of NB-NGL distribution is carry out on three samples of medical data, industry data, and insurance data. Based on the results, it is shown that the proposed distribution provides a better fit compared to the Poisson, negative binomial, and its sub-model for count data.

Bayesian inference for the negative binomial-generalized Lindley regression model: properties and applications

This article aims to develop a new linear model for count data, which is called the negative binomial - generalized Lindley (NB-GL) regression model. The NB-GL distribution has been proposed and applied to count data analysis, which is constructed as a mixture of the negative binomial and generalized Lindley distributions. The NB-GL distribution has the special sub-models, such as the negative binomial - Lindley, negative binomial - gamma, and negative binomial - exponential distributions. Parameters of the distribution and its regression model are estimated using a Bayesian approach. The NB-GL regression model is applied to fit real data sets. Its performance is compared with some traditional models. The results show that the generalized linear model for the NB-GL model describes the data sets better than other models.

New class of Lindley distributions: properties and applications

A new generalized class of Lindley distribution is introduced in this paper. This new class is called the T-Lindley{Y} class of distributions, and it is generated by using the quantile functions of uniform, exponential, Weibull, log-logistic, logistic and Cauchy distributions. The statistical properties including the modes, moments and Shannon’s entropy are discussed. Three new generalized Lindley distributions are investigated in more details. For estimating the unknown parameters, the maximum likelihood estimation has been used and a simulation study was carried out. Lastly, the usefulness of this new proposed class in fitting lifetime data is illustrated using four different data sets. In the application section, the strength of members of the T-Lindley{Y} class in modeling both unimodal as well as bimodal data sets is presented. A member of the T-Lindley{Y} class of distributions outperformed other known distributions in modeling unimodal and bimodal lifetime data sets.

A new two-parameter discrete poisson-generalized Lindley distribution with properties and applications to healthcare data sets

Mixed-Poisson distributions have been used in many fields for modeling the over-dispersed count data sets. To open a new opportunity in modeling the over-dispersed count data sets, we introduce a new mixed-Poisson distribution using the generalized Lindley distribution as a mixing distribution. The moment and probability generating functions, factorial moments as well as skewness, and kurtosis measures are derived. Using the mean-parametrized version of the proposed distribution, we introduce a new count regression model which is an appropriate model for over-dispersed counts. The healthcare data sets are analyzed employing a new count regression model. We conclude that the new regression model works well in the case of over-dispersion.

On a new generalized lindley distribution: Properties, estimation and applications.

In this study, an extension of the generalized Lindley distribution using the Marshall-Olkin method and its own sub-models is presented. This new model for modelling survival and lifetime data is flexible. Several statistical properties and characterizations of the subject distribution along with its reliability analysis are presented. Statistical inference for the new family such as the Maximum likelihood estimators and the asymptotic variance covariance matrix of the unknown parameters are discussed. A simulation study is considered to compare the efficiency of the different estimators based on mean square error criterion. Finally, a real data set is analyzed to show the flexibility of our proposed model compared with the fit attained by some other competitive distributions.

Inference on Exponentiated Power Lindley Distribution Based on Order Statistics with Application

Exponentiated power Lindley distribution is proposed as a generalization of some widely well-known distributions such as Lindley, power Lindley, and generalized Lindley distributions. In this paper, the exact explicit expressions for moments of order statistics from the exponentiated power Lindley distribution are derived. By using these relations, the best linear unbiased estimates of the location and scale parameters, based on type-II right-censored sample, are obtained. Next, the mean, variance, and coefficients of skewness and kurtosis of some certain linear functions of order statistics are calculated and then used to derive the approximate confidence interval for the location and scale parameters using the Edgeworth approximation. Finally, some numerical illustrations and two real data applications are presented.

Performance analysis of metaheuristic optimization algorithms in estimating the parameters of several wind speed distributions

For a better use of wind energy, the accurate selection of the wind speed distributions that best represents the regarding wind regime’s characteristics is essential. The Weibull distribution is the most common, but this model is not always the most suitable. Therefore, in order to obtain more reliable information, the evaluation of different distributions becomes necessary. Another crucial step is the estimation of the parameters that govern these distributions because the accuracy of these estimates directly affects the energy generation calculations. In the last few years, different optimization methods have been used for this purpose. However, the applications of these methods are focused on conventional two-parameter distributions, such as Weibull and Lognormal. Futhermore, different authors report that there is a lack of studies that use optimization methods for this purpose. In this paper, four metaheuristic optimization algorithms (MOA)—namely, Migrating Birds Optimization (MBO), Imperialist Competitive Algorithm (ICA), Harmony Search (HS) and Cuckoo Search (CS)—are used to fit 11 distributions in two Brazillian regions. Thus, this work expands the application of the MOA to beyond the conventional distributions and applies, for the first time, the MBO and ICA in estimating the parameters of wind speed distributions, thereby introducing new ways to optimize the use of wind resources. The fits obtained by the MOA were compared with those obtained by the method Maximum Likelihood Estimation (MLE). Gamma Generalized and Extended Generalized Lindley distributions presented the best fits, and the MOA outperformed the MLE because the global score values obtained were smaller.

Inference for generalized inverse Lindley distribution based on generalized order statistics

This article addresses the problem of deriving the explicit expressions for single and product moments of order statistics, generalized order statistics and dual generalized order statistics from the generalized Lindley distribution. The means and variances of order statistics, lower record values and progressively type-II censored order statistics for various values of the parameters are tabulated. Furthermore, the maximum likelihood estimators for the parameters of the model using generalized order statistics are obtained. The Bayes estimators under squared error and LINEX (Linear exponential) loss functions using Markov Chain Monte Carlo (MCMC) technique are obtained. Finally, three real data examples to lower record values, type-II censored and progressively type-II censored order statistics have been analyzed for illustrative purposes.

Statistical inference based on generalized Lindley record values

This paper addresses the problems of frequentist and Bayesian estimation for the unknown parameters of generalized Lindley distribution based on lower record values. We first derive the exact explicit expressions for the single and product moments of lower record values, and then use these results to compute the means, variances and covariance between two lower record values. We next obtain the maximum likelihood estimators and associated asymptotic confidence intervals. Furthermore, we obtain Bayes estimators under the assumption of gamma priors on both the shape and the scale parameters of the generalized Lindley distribution, and associated the highest posterior density interval estimates. The Bayesian estimation is studied with respect to both symmetric (squared error) and asymmetric (linear-exponential (LINEX)) loss functions. Finally, we compute Bayesian predictive estimates and predictive interval estimates for the future record values. To illustrate the findings, one real data set is analyzed, and Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation and prediction.

A New Heavy Tailed Class of Distributions Which Includes the Pareto

In this paper, a new heavy-tailed distribution, the mixture Pareto-loggamma distribution, derived through an exponential transformation of the generalized Lindley distribution is introduced. The resulting model is expressed as a convex sum of the classical Pareto and a special case of the loggamma distribution. A comprehensive exploration of its statistical properties and theoretical results related to insurance are provided. Estimation is performed by using the method of log-moments and maximum likelihood. Also, as the modal value of this distribution is expressed in closed-form, composite parametric models are easily obtained by a mode matching procedure. The performance of both the mixture Pareto-loggamma distribution and composite models are tested by employing different claims datasets.

Generalized Lindley Distribution Based on Order Statistics and Associated Inference with Application

The generalized Lindley distribution is an important distribution for analyzing the stress–strength reliability models and lifetime data, which is quite flexible and can be used effectively in modeling survival data. It can have increasing, decreasing, upside-down bathtub and bathtub shaped failure rate. In this paper, we derive the exact explicit expressions for the single, double (product), triple and quadruple moments of order statistics from the generalized Lindley distribution. By using these relations, we have tabulated the expected values, second moments, variances and covariances of order statistics from samples of sizes up to 10 for various values of the parameters. Also, we use these moments to obtain the best linear unbiased estimates of the location and scale parameters based on Type-II right-censored samples. In addition, we carry out some numerical illustrations through Monte Carlo simulations to show the usefulness of the findings. Finally, we apply the findings of the paper to some real data set.

A New Probability Model for Hydrologic Events: Properties and Applications

Upon the motivation of unstable climatic conditions of the world like excess of rains, drought and huge floods, we introduce a versatile hydrologic probability model with two scale parameters. The proposed model contains Lindley and exponentiated exponential (Lindley in J R Stat Soc Ser B 20:102–107, 1958; Gupta and Kundu in Biom J 43(1):117–130, 2001) distributions as special cases. Various properties of the distribution are obtained, such as shapes of the density and hazard functions, moments, mean deviation, information-generating function, conditional moments, Shannon entropy, L-moments, order statistics, information matrix and characterization via hazard function. Parameters are estimated via maximum likelihood estimation method. A simulation scheme is provided for generating the random data from the proposed distribution. Four data sets are used for comparing the proposed model with a set of well-known hydrologic models, such as generalized Pareto, log normal (3), log Pearson type III, Kappa(3), Gumbel, generalized logistic and generalized Lindley distributions, using some goodness-of-fit tests. These comparisons render the proposed model suitable and representative for hydrologic data sets with least loss of information attitude and a realistic return period, which render it as an appropriate alternate of the existing hydrologic models. Supplementary materials for this paper are available online.

Generalized Lindley and Power Lindley distributions for modeling the wind speed data

In this study, we propose to use Generalized Lindley (GL) and Power Lindley (PL) distributions as an alternative to the Weibull distribution for modeling the wind speed data. In the application part of the study, we consider the actual wind speed data collected in hourly basis from the Bilecik, Bursa, Eskisehir and Sakarya sites, Turkey in 2009. These data sets are modeled by using GL and PL distributions. To compare their modeling performance with well known and widely used Weibull distribution, Weibull distribution is also included into the study. The results show that GL distribution provides the best fitting according to root mean square error (RMSE), coefficient of determination (R2), maximum value of the likelihood function corresponding to the ML estimates of the parameters (lnL) and Akaike information criterion (AIC). It is also seen that PL distribution is preferable in terms of power density error (PDE) criterion.

New Extended Generalized Lindley Distribution: Properties and Applications

In this paper, we introduce a new extended generalized Lindley distribution ($NEGLD$). Some statistical properties of the proposed distribution are explicitly derived. These include conditional moments, vitality function, geometric vitality function, mean inactivity time and various entropy measures. Maximum likelihood estimation, moment estimation and asymptotic confidence interval are used for estimating the parameters. The distribution has been fitted to a data set to test its goodness of fit and it has been found that this distribution gives better fit than the some other well-known existing distributions.

The Exponentiated Generalized Lindley Distribution

The Exponentiated Generalized Lindley Distribution

On a multivariate Lindley distribution

ABSTRACTThis article proposes a multivariate extension of the generalized Lindley distribution introduced by Abouammoh et al. (2015). The proposed model is based on a probabilistic construction in which several Lindley random variables are connected by a common shock. Many statistical properties of this new distribution are explored. In particular, explicit forms of product moments, moment-generating function, and conditional moments are derived. Explicit expressions of moment-based estimators of the underlying parameters of the proposed model are established. Estimation using the maximum likelihood procedure is also investigated. Simulations attesting to the quality of the proposed estimators are presented. Application of the proposed model in reliability is also discussed.