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

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

2018 ◽  
Vol 10 (2) ◽  
pp. 145-157
Author(s):  
R. Shanker ◽  
K. K. Shukla

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).


2019 ◽  
Vol 11 (1) ◽  
pp. 1-13
Author(s):  
R. Shanker ◽  
K. K. Shukla

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).


2019 ◽  
Vol 12 (02) ◽  
pp. 1950013
Author(s):  
Rama Shanker ◽  
Kamlesh Kumar Shukla

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.


2020 ◽  
Vol 1 ◽  
pp. 33-42
Author(s):  
Rama Shanker ◽  
Umme Habibah Rahman

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.


2020 ◽  
Vol 9 (1) ◽  
pp. 1-4
Author(s):  
Rama Shanker ◽  
Kamlesh Kumar Shukla

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.


Author(s):  
Duha Hamed ◽  
Ahmad Alzaghal

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.


Author(s):  
Barinaadaa John Nwikpe ◽  
Isaac Didi Essi

A new two-parameter continuous distribution called the Two-Parameter Nwikpe (TPAN) distribution is derived in this paper. The new distribution is a mixture of gamma and exponential distributions. A few statistical properties of the new probability distribution have been derived. The shape of its density for different values of the parameters has also been established.  The first four crude moments, the second and third moments about the mean of the new distribution were derived using the method of moment generating function. Other statistical properties derived include; the distribution of order statistics, coefficient of variation and coefficient of skewness. The parameters of the new distribution were estimated using maximum likelihood method. The flexibility of the Two-Parameter Nwikpe (TPAN) distribution was shown by fitting the distribution to three real life data sets. The goodness of fit shows that the new distribution outperforms the one parameter exponential, Shanker and Amarendra distributions for the data sets used for this study.


2011 ◽  
Vol 48 (A) ◽  
pp. 367-378 ◽  
Author(s):  
Paul Embrechts ◽  
Thomas Liniger ◽  
Lu Lin

A Hawkes process is also known under the name of a self-exciting point process and has numerous applications throughout science and engineering. We derive the statistical estimation (maximum likelihood estimation) and goodness-of-fit (mainly graphical) for multivariate Hawkes processes with possibly dependent marks. As an application, we analyze two data sets from finance.


Author(s):  
Arun Kumar Chaudhary ◽  
Vijay Kumar

Here, in this paper, a continuous distribution called ArcTan Lomax distribution with three-parameter has been introduced along with some relevant properties of statistics and mathematics pertaining to the distribution. With the help of three established estimations methods including maximum likelihood estimation (MLE), estimation of the presented distribution’s model parameters is done. Also with the help of a real set of data, the distribution’s goodness-of-fit is examined in contrast to some established models in survival analysis.


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