The discrete Lindley distribution: properties and applications

Gómez–Déniz, Emilio; Calderín–Ojeda, Enrique

doi:10.1080/00949655.2010.487825

Cited by 151 publications

(55 citation statements)

References 19 publications

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“…As for the continuous multivariate version, there were Kotz et al (2000) and Kotz and Nadarajah (2004). For the discrete version, see Johnson et al (1997), Gómez-Déniz et al (2012) and Sarabia and Gómez-Déniz (2011), among others. Then there were Cuadras (1992) and Dolati and Úbeda-Flores (2005) for constructing distributions with given multivariate marginals and given dependence structure.…”

Section: Journal Of Statistical Planning and Inference (November 2009)mentioning

confidence: 99%

Recent developments on the construction of bivariate distributions with fixed marginals

Lin

Dou

Kuriki

et al. 2014

J Stat Distrib Appl

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Constructing a bivariate distribution with specific marginals and correlation has been a challenging problem since 1930s. In this survey we shall focus on the recent developments on the FGM-related distributions, including Sarmanov and Lee's distributions, Baker's distributions and Bayramoglu's distributions. This complements the most recent works of (i) the review by Sarabia and Gómez-Déniz (2008, SORT) and (ii) the monograph by Balakrishnan and Lai (2009, Springer). Some new results are provided. Mathematics Subject Classification (2000): 62H20; 62H86; 62G30; 60E05; 62E10

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Section: Journal Of Statistical Planning and Inference (November 2009)mentioning

confidence: 99%

Recent developments on the construction of bivariate distributions with fixed marginals

Lin

Dou

Kuriki

et al. 2014

J Stat Distrib Appl

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show abstract

“…Most observed frequencies provide (y 1 , 0) and (0, y 2 ) data, indicating negative correlation between y 1 and y 2 . Therefore, we fit BP (Lakshminarayana et al, 1999), BNB (Famoye, 2010) and BPL (Gomez-Deniz et al, 2012) distributions to the data since these distributions can be fitted to bivariate data with positive, zero or negative correlation.…”

Section: Several Testsmentioning

confidence: 99%

“…The Bivariate Negative Binomial (BNB), Bivariate PoissonLognormal (BPLN), Bivariate Poisson-Inverse Gaussian (BPIG) and bivariate Poisson-Lindley (BPL) distributions are several examples of classes of mixed distribution which are extended from univariate case. For further literatures, BNB distribution was studied in Marshall and Olkin (1990) and applied in Karlis and Ntzoufras (2003), tests for overdispersion and independence in BNB model were discussed in Cheon et al, 2009), BPIG distribution was derived by Stein et al (1987), BPL distribution was proposed by Gomez-Deniz et al (2012) and Bivariate Poisson-Weighted Exponential (BPWE) was proposed in Zamani et al (2014b).…”

Section: Introductionmentioning

confidence: 99%

Bivariate Poisson-Lindley Distribution with Application

Zamani¹,

Faroughi

Ismail³

2015

Journal of Mathematics and Statistics

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This study applies a Bivariate Poisson-Lindley (BPL) distribution for modeling dependent and over-dispersed count data. The advantage of using this form of BPL distribution is that the correlation coefficient can be positive, zero or negative, depending on the multiplicative factor parameter. Several properties such as mean, variance and correlation coefficient of the BPL distribution are discussed. A numerical example is given and the BPL distribution is compared to Bivariate Poisson (BP) and Bivariate Negative Binomial (BNB) distributions which also allow the correlation coefficient to be positive, zero or negative. The results show that BPL distribution provides the smallest Akaike Information Criterion (AIC), indicating that the distribution can be used as an alternative for fitting dependent and over-dispersed count data, with either negative or positive correlation.

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“…For example, we can address the works of [12], [15], [9] and [10] which are the discrete versions of Weibull, Rayleigh, half-normal and Burr distributions, respectively. A discrete version of Lindley distribution is introduced by [7] and [4]. [13] obtained a new discrete distribution by discretizing generalized exponential distribution of [8].…”

Section: Introductionmentioning

confidence: 99%

Exponentiated generalized geometric distribution: A new discrete distribution

Bidram¹,

Roozegar²,

Nekoukhou³

2015

HJMS

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In this paper, a new three-parameter extension of the generalized geometric distribution of [6] is introduced. The new discrete distribution belongs to the resilience parameter family and handles a decreasing, increasing, upside-down and bathtub-shaped hazard rate function. The new distributions can also be considered as discrete analogs of some recent continuous distributions belonging to the known Marshall-Olkin family. Here, some basic statistical and mathematical properties of the new distribution are studied. In addition, estimation of the unknown parameters, a simulated example and an application of the new model are illustrated.

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The discrete Lindley distribution: properties and applications

Cited by 151 publications

References 19 publications

Recent developments on the construction of bivariate distributions with fixed marginals

Recent developments on the construction of bivariate distributions with fixed marginals

Bivariate Poisson-Lindley Distribution with Application

Exponentiated generalized geometric distribution: A new discrete distribution

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