An alternative version of zero-inflated logarithmic series distribution and some of its applications

Kumar, C. Satheesh; Riyaz, A.

doi:10.1080/00949655.2013.867347

Cited by 6 publications

(2 citation statements)

References 8 publications

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“…Note that in this family, the zero point is not included in support of the distribution. Kumar and Riyaz (2013, 2014) used a modified version of this distribution to model the zero inflated data.…”

Section: Three Subfamilies Of the Mzkips Distributionmentioning

confidence: 99%

Flexible multivariate zero to k inflated power series regression model with applications

Saboori

Doostparast

2022

Stat

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Inflated distributions are applied in various fields, including insurance, traffic networks and survival analyses. First, they are defined by a baseline discrete distribution, and then, extra masses are added to some points of interest, called inflated points, to achieve more flexible models for data analyses. The baseline distribution is arbitrary and application dependent. Here, the rich family of power series distributions is considered as the baseline, which includes various common discrete distributions such as Poisson, negative binomial, multinomial and logarithmic series distributions. This paper deals with an extension of previous works in two directions. The former is an extension of the univariate inflated distributions to multivariate ones, and the latter is the generalization of the inflated points from the zero single point to the set k=0,1,…. Under this setting, various inflated distributions in the literature fall into the proposed family of distributions. These extensions make the proposed model flexible and practically useful in data analyses. To do this, the problem of estimating parameters with various approaches as well as hypotheses testing is studied in detail. Multivariate‐generalized linear models with inflated multivariate discrete responses are also discussed. To assess the performance of the proposed family of inflated distributions, simulation studies are conducted, and a real data set on an Australian health survey study is also analysed.

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Section: Three Subfamilies Of the Mzkips Distributionmentioning

confidence: 99%

Flexible multivariate zero to k inflated power series regression model with applications

Saboori

Doostparast

2022

Stat

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“…Various generalized versions of the LSD have been proposed in the literature. For example see Gupta (1985, 1988), Ong (2000), Khang and Ong (2007) and Kumar and Riyaz (2013).…”

Section: Introductionmentioning

confidence: 99%

On Estimating the Parameters of an Extended Form of Logarithmic Series Distribution

Kumar¹,

Riyaza²

2013

Communications for Statistical Applications and Methods

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We consider an extended version of a logarithmic series distribution and discuss the estimation of its parameters by the method of moments and the method of maximum likelihood. Test procedures are suggested to test the significance of the additional parameter of this distribution and all procedures are illustrated with the help of real life data sets. In addition, a simulation study is conducted to assess the performance of the estimators.

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An order k version of the alternative zero-inflated logarithmic series distribution and its applications

Kumar

Riyaz

2016

Journal of Applied Statistics

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An alternative version of zero-inflated logarithmic series distribution and some of its applications

Cited by 6 publications

References 8 publications

Flexible multivariate zero to k inflated power series regression model with applications

Flexible multivariate zero to k inflated power series regression model with applications

On Estimating the Parameters of an Extended Form of Logarithmic Series Distribution

An order k version of the alternative zero-inflated logarithmic series distribution and its applications

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