A New Zero–One-Inflated Poisson–Lindley Distribution for Modelling Overdispersed Count Data

2022 ◽  
Author(s):  
Razik Ridzuan Mohd Tajuddin ◽  
Noriszura Ismail ◽  
Kamarulzaman Ibrahim ◽  
Shaiful Anuar Abu Bakar
Keyword(s):  
Count Data ◽  
Lindley Distribution

A four-parameter negative binomial-Lindley distribution for modeling over and underdispersed count data with excess zeros

2020 ◽  
pp. 1-13
Author(s):  
Razik Ridzuan Mohd Tajuddin ◽  
Noriszura Ismail ◽  
Kamarulzaman Ibrahim ◽  
Shaiful Anuar Abu Bakar
Keyword(s):  
Count Data ◽  
Negative Binomial ◽  
Lindley Distribution ◽  
Excess Zeros

Poisson size-biased Lindley distribution and its applications

2021 ◽  
Author(s):  
Showkat Ahmad Dar ◽  
Anwar Hassan ◽  
Peer Bilal Ahmad
Keyword(s):  
Parameter Estimation ◽  
Count Data ◽  
Hazard Rate ◽  
Risk Model ◽  
Probability Generating Function ◽  
Likelihood Estimation ◽  
Lindley Distribution ◽  
Collective Risk Model ◽  
Collective Risk ◽  
Erlang Distributions

In this paper, a new model for count data is introduced by compounding the Poisson distribution with size-biased three-parameter Lindley distribution. Statistical properties, such as reliability, hazard rate, reverse hazard rate, Mills ratio, moments, shewness, kurtosis, moment genrating function, probability generating function and order statistics, have been discussed. Moreover, the collective risk model is discussed by considering the proposed distrubution as the primary distribution and the expoential and Erlang distributions as the secondary ones. Parameter estimation is done using maximum likelihood estimation (MLE). Finally a real dataset is discussed to demonstrate the suitability and applicability of the proposed distribution in modeling count dataset.

A generalization of Poisson-Sujatha distribution and its applications to ecology

2019 ◽  
Vol 12 (02) ◽  
pp. 1950013
Author(s):  
Rama Shanker ◽  
Kamlesh Kumar Shukla
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Poisson Distribution ◽  
Count Data ◽  
Coefficient Of Variation ◽  
Goodness Of Fit ◽  
Likelihood Estimation ◽  
Lindley Distribution ◽  
Index Of Dispersion

A generalization of Poisson Sujatha distribution (AGPSD), which includes Poisson-Lindley distribution (PLD) and Poisson-Sujatha distribution (PSD) as particular cases, has been proposed and studied. Its moments and moments-based measures including coefficient of variation, skewness, kurtosis and index of dispersion have been obtained and their behaviors have been discussed. The estimation of its parameters has been discussed with maximum likelihood estimation. The applications of the proposed distribution has been explained through two examples of count data from ecology and the goodness of fit of the distribution has been compared with Poisson distribution, PLD and PSD.

scholarly journals A Noncentral Lindley Construction Illustrated in an INAR(1) Environment

Stats ◽  
2022 ◽  
Vol 5 (1) ◽  
pp. 70-88
Author(s):  
Johannes Ferreira ◽  
Ané van der Merwe
Keyword(s):  
Time Series ◽  
Discrete Time ◽  
Count Data ◽  
Structural Characteristics ◽  
Poisson Model ◽  
Real Data ◽  
Error Distribution ◽  
Noncentrality Parameter ◽  
Lindley Distribution ◽  
Count Model

This paper proposes a previously unconsidered generalization of the Lindley distribution by allowing for a measure of noncentrality. Essential structural characteristics are investigated and derived in explicit and tractable forms, and the estimability of the model is illustrated via the fit of this developed model to real data. Subsequently, this model is used as a candidate for the parameter of a Poisson model, which allows for departure from the usual equidispersion restriction that the Poisson offers when modelling count data. This Poisson-noncentral Lindley is also systematically investigated and characteristics are derived. The value of this count model is illustrated and implemented as the count error distribution in an integer autoregressive environment, and juxtaposed against other popular models. The effect of the systematically-induced noncentrality parameter is illustrated and paves the way for future flexible modelling not only as a standalone contender in continuous Lindley-type scenarios but also in discrete and discrete time series scenarios when the often-encountered equidispersed assumption is not adhered to in practical data environments.

Regression Analysis of Count Data

1998 ◽  
Author(s):  
A. Colin Cameron ◽  
Pravin K. Trivedi
Keyword(s):  
Regression Analysis ◽  
Count Data

Analyzing discontinuities in longitudinal count data: A multilevel generalized linear mixed model.

2020 ◽  
Author(s):  
James L. Peugh ◽  
Sarah J. Beal ◽  
Meghan E. McGrady ◽  
Michael D. Toland ◽  
Constance Mara
Keyword(s):  
Count Data ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Generalized Linear Mixed Model ◽  
Longitudinal Count Data

Exploring Attendance at a Traditional Cultural Event: The Case of a Holy Week Celebration

2020 ◽  
Vol 24 (1) ◽  
pp. 153-168
Author(s):  
Víctor Lafuente ◽  
José Ángel Sanz ◽  
María Devesa
Keyword(s):  
Cultural Capital ◽  
Cultural Heritage ◽  
Count Data ◽  
Data Model ◽  
Social Aspects ◽  
Social Nature ◽  
The World ◽  
Local Residents ◽  
The City ◽  
Complex Expression

Holy Week is one of the most important traditions in many parts of the world and a complex expression of cultural heritage. The main goal of this article is to explore which factors determine participation in Holy Week celebrations in the city of Palencia (Spain), measured through the number of processions attended. For this purpose, an econometric count data model is used. Variables included in the model not only reflect participants' sociodemographic features but other factors reflecting cultural capital, accumulated experience, and social aspects of the event. A distinction is drawn between three types of participants: brotherhood members, local residents, and visitors, among whom a survey was conducted to collect the information required. A total of 248 surveys were carried out among brotherhood members, 209 among local residents, and 259 among visitors. The results confirm the religious and social nature of this event, especially in the case of local participants. However, in the case of visitors, participation also depends on aspects reflecting the celebration's cultural and tourist dimension—such as visiting other religious and cultural attractions—suggesting the existence of specific tourism linked to the event. All of this suggests the need to manage the event, ensuring a balance is struck between the various stakeholders' interests and developing a tourist strategy that prioritizes public-private cooperation.

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