scholarly journals A new three-parameter size-biased poisson-lindley distribution with properties and applications

2020 ◽  
Vol 9 (1) ◽  
pp. 1-4
Author(s):  
Rama Shanker ◽  
Kamlesh Kumar Shukla
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Negative Binomial Distribution ◽  
Coefficient Of Variation ◽  
Goodness Of Fit ◽  
Negative Binomial ◽  
Geometric Distribution ◽  
Likelihood Estimation ◽  
Lindley Distribution ◽  
Two Parameter

A new three-parameter size-biased Poisson-Lindley distribution which includes several one parameter and two-parameter size-biased distributions including size-biased geometric distribution (SBGD), size-biased negative binomial distribution (SBNBD), size-biased Poisson-Lindley distribution (SBPLD), size-biased Poisson-Shanker distribution (SBPSD), size-biased two-parameter Poisson-Lindley distribution-1 (SBTPPLD-1), size-biased two-parameter Poisson-Lindley distribution-2(SBTPPLD-2), size-biased quasi Poisson-Lindley distribution (SBQPLD) and size-biased new quasi Poisson-Lindley distribution (SBNQPLD) for particular cases of parameters has been proposed. Its various statistical properties based on moments including coefficient of variation, skewness, kurtosis and index of dispersion have been studied. Maximum likelihood estimation has been discussed for estimating the parameters of the distribution. Goodness of fit of the proposed distribution has been discussed.

scholarly journals On Poisson-Weighted Lindley Distribution and Its Applications

2019 ◽  
Vol 11 (1) ◽  
pp. 1-13
Author(s):  
R. Shanker ◽  
K. K. Shukla
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Negative Binomial Distribution ◽  
Goodness Of Fit ◽  
Negative Binomial ◽  
Likelihood Estimation ◽  
Poisson Mixture ◽  
Lindley Distribution ◽  
Generalized Poisson ◽  
And Behavior

In this paper the nature and behavior of its coefficient of variation, skewness, kurtosis and index of dispersion of Poisson- weighted Lindley distribution (P-WLD), a Poisson mixture of weighted Lindley distribution, have been proposed and the nature and behavior have been explained graphically. Maximum likelihood estimation has been discussed to estimate its parameters. Applications of the proposed distribution have been discussed and its goodness of fit has been compared with Poisson distribution (PD), Poisson-Lindley distribution (PLD), negative binomial distribution (NBD) and generalized Poisson-Lindley distribution (GPLD).

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 Zero-Truncated Discrete Two-Parameter Poisson-Lindley Distribution with Applications

2018 ◽  
Vol 22 (2) ◽  
pp. 76-85
Author(s):  
Rama Shanker ◽  
Kamlesh Kumar Shukla
Keyword(s):  
Maximum Likelihood ◽  
Poisson Distribution ◽  
Goodness Of Fit ◽  
Continuous Distribution ◽  
Likelihood Estimation ◽  
Data Sets ◽  
Lindley Distribution ◽  
Coefficients Of Variation ◽  
And Behavior ◽  
Two Parameter

A zero-truncated discrete two-parameter Poisson-Lindley distribution (ZTDTPPLD), which includes zero-truncated Poisson-Lindley distribution (ZTPLD) as a particular case, has been introduced. The proposed distribution has been obtained by compounding size-biased Poisson distribution (SBPD) with a continuous distribution. Its raw moments and central moments have been given. The coefficients of variation, skewness, kurtosis, and index of dispersion have been obtained and their nature and behavior have been studied graphically. Maximum likelihood estimation (MLE) has been discussed for estimating its parameters. The goodness of fit of ZTDTPPLD has been discussed with some data sets and the fit shows satisfactory over zero – truncated Poisson distribution (ZTPD) and ZTPLD. Journal of Institute of Science and TechnologyVolume 22, Issue 2, January 2018, Page: 76-85

scholarly journals A New Two-Parameter Lindley Distribution

2020 ◽  
Vol 1 ◽  
pp. 33-42
Author(s):  
Rama Shanker ◽  
Umme Habibah Rahman
Keyword(s):  
Maximum Likelihood ◽  
Goodness Of Fit ◽  
Fisher Information Matrix ◽  
Information Matrix ◽  
Likelihood Estimation ◽  
Lifetime Data ◽  
Lindley Distribution ◽  
Method Of Maximum Likelihood ◽  
Two Parameter ◽  
Family Of Distributions

In this paper, a new two-parameter Lindley distribution has been proposed. Descriptive statistical properties along with order statistics, Fisher information matrix and confidence interval of the proposed distribution have been discussed. Parameters are estimated by the method of Maximum Likelihood estimation. A real lifetime data has been presented to test the goodness of fit of the proposed distribution over other one parameter and two –parameter Lindley family of distributions.

A Generalized Size-Biased Poisson-Lindley Distribution and Its Applications to Model Size Distribution of Freely-Forming Small Group

2018 ◽  
Vol 10 (2) ◽  
pp. 145-157
Author(s):  
R. Shanker ◽  
K. K. Shukla
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Size Distribution ◽  
Poisson Distribution ◽  
Goodness Of Fit ◽  
Likelihood Estimation ◽  
Lindley Distribution ◽  
Coefficients Of Variation ◽  
Model Size ◽  
And Behavior

In this paper, generalized size-biased Poisson-Lindley distribution (GSBPLD) which includes size-biased Poisson-Lindley distribution (SBPLD) as particular case, has been proposed and studied. Its moments based measures including coefficients of variation, skewness, kurtosis, and index of dispersion have been derived and their nature and behavior have been discussed with varying values of the parameters. The estimation of its parameter has been discussed using maximum likelihood estimation. Some applications of the proposed distribution have been explained through datasets relating to size distribution of freely-forming and the goodness of fit has been found satisfactory over SBPLD and size-biased Poisson distribution (SBPD).

scholarly journals Identifying Stabilising Effects on Survey Based Life Satisfaction Using Quasi-maximum Likelihood Estimation

2021 ◽  
Author(s):  
Johannes Klement
Keyword(s):  
Life Satisfaction ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Negative Binomial ◽  
Measurement Instrument ◽  
Likelihood Estimation ◽  
Satisfaction Scale ◽  
Quasi Maximum Likelihood ◽  
The Stability

AbstractTo which extent do happiness correlates contribute to the stability of life satisfaction? Which method is appropriate to provide a conclusive answer to this question? Based on life satisfaction data of the German SOEP, we show that by Negative Binomial quasi-maximum likelihood estimation statements can be made as to how far correlates of happiness contribute to the stabilisation of life satisfaction. The results show that happiness correlates which are generally associated with a positive change in life satisfaction, also stabilise life satisfaction and destabilise dissatisfaction with life. In such as they lower the probability of leaving positive states of life satisfaction and increase the probability of leaving dissatisfied states. This in particular applies to regular exercise, volunteering and living in a marriage. We further conclude that both patterns in response behaviour and the quality of the measurement instrument, the life satisfaction scale, have a significant effect on the variation and stability of reported life satisfaction.

scholarly journals New class of Lindley distributions: properties and applications

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Duha Hamed ◽  
Ahmad Alzaghal
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Simulation Study ◽  
Likelihood Estimation ◽  
Statistical Properties ◽  
Data Sets ◽  
Lifetime Data ◽  
Unknown Parameters ◽  
Lindley Distribution ◽  
New Class

AbstractA 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.

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