scholarly journals A Two Parameter Discrete Lindley Distribution

2016 ◽  
Vol 39 (1) ◽  
pp. 45-61 ◽  
Author(s):  
Tassaddaq Hussain ◽  
Muhammad Aslam ◽  
Munir Ahmad
Keyword(s):  
Negative Binomial ◽  
Parameters Estimation ◽  
Discrete Distributions ◽  
Likelihood Method ◽  
Data Sets ◽  
Factorial Moments ◽  
Lindley Distribution ◽  
Generalized Poisson ◽  
Gamma Distributions ◽  
Two Parameter

<p>In this article we have proposed and discussed a two parameter discrete Lindley distribution. The derivation of this new model is based on a two step methodology i.e. mixing then discretizing, and can be viewed as a new generalization of geometric distribution. The proposed model has proved itself as the least loss of information model when applied to a number of data sets (in an over and under dispersed structure). The competing models such as Poisson, Negative binomial, Generalized Poisson and discrete gamma distributions are the well known standard discrete distributions. Its Lifetime classification, kurtosis, skewness, ascending and descending factorial moments as well as its recurrence relations, negative moments, parameters estimation via maximum likelihood method, characterization and discretized bi-variate case are presented.</p>

scholarly journals A New Discrete Analog of the Continuous Lindley Distribution, with Reliability Applications

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 603
Author(s):  
Abdulhakim A. Al-Babtain ◽  
Abdul Hadi N. Ahmed ◽  
Ahmed Z. Afify
Keyword(s):  
Goodness Of Fit ◽  
Negative Binomial ◽  
Real Data ◽  
Moment Generating Function ◽  
Discrete Analog ◽  
Bias Reduction ◽  
Discrete Distributions ◽  
Likelihood Method ◽  
Probability Mass Function ◽  
Lindley Distribution

In this paper, we propose and study a new probability mass function by creating a natural discrete analog to the continuous Lindley distribution as a mixture of geometric and negative binomial distributions. The new distribution has many interesting properties that make it superior to many other discrete distributions, particularly in analyzing over-dispersed count data. Several statistical properties of the introduced distribution have been established including moments and moment generating function, residual moments, characterization, entropy, estimation of the parameter by the maximum likelihood method. A bias reduction method is applied to the derived estimator; its existence and uniqueness are discussed. Applications of the goodness of fit of the proposed distribution have been examined and compared with other discrete distributions using three real data sets from biological sciences.

scholarly journals A Distribuição Half-Normal Generalizada Discreta: uma distribuição alternativa na análise de dados de contagem

2019 ◽  
Vol 41 ◽  
pp. 27
Author(s):  
Josmar Mazucheli ◽  
Ricardo Puziol De Oliveira ◽  
Jean Carlos Cardoso
Keyword(s):  
Maximum Likelihood Method ◽  
Negative Binomial ◽  
Survival Function ◽  
Discrete Distributions ◽  
Likelihood Method ◽  
Discrete Version ◽  
Data Sets ◽  
Continuous Version ◽  
Binomial Distributions ◽  
General Data

In general, data that are obtained by counting processes, strictly discrete or discretized (from truncations and/or rounding), are analyzed, without exhaustion, by the Geometric, Logarithmic, Poisson and Negative Binomial distributions. In recent years a large number of discrete distributions have been proposed in the literature from the discretization of continuous random variables. Many of the discretization methods preserve one or more characteristics of the continuous version, with the proposal of Nakagawa e Osaki (1975) being the most used. In this paper, from this methodology, which makes use of the survival function, we propose the discrete version of the continuous generalized Half-Normal distribution, introduced in the literature by Cooray e Ananda (2008). Some of its properties are discussed and Monte Carlo simulations evaluate the bias and accuracy of the estimates obtained by the maximum likelihood method and method of moments. Some discrete data sets found in the literature are considered to illustrate the applicability of the proposed distribution.

scholarly journals Two-Parameter Nwikpe (TPAN) Distribution with Application

2021 ◽  
pp. 56-67
Author(s):  
Barinaadaa John Nwikpe ◽  
Isaac Didi Essi
Keyword(s):  
Goodness Of Fit ◽  
Continuous Distribution ◽  
Real Life ◽  
Moment Generating Function ◽  
Statistical Properties ◽  
Likelihood Method ◽  
Data Sets ◽  
Method Of Moment ◽  
Two Parameter ◽  
New Distribution

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.

scholarly journals A Generalised Exponential-Lindley Mixture of Poisson Distribution

2019 ◽  
Vol 3 ◽  
pp. 11-20
Author(s):  
Binod Kumar Sah ◽  
A. Mishra
Keyword(s):  
Poisson Distribution ◽  
Negative Binomial ◽  
Probability Distributions ◽  
Mixture Distribution ◽  
Discrete Data ◽  
Likelihood Method ◽  
P Value ◽  
Data Set ◽  
Lindley Distribution ◽  
First Four Moments

Background: The exponential and the Lindley (1958) distributions occupy central places among the class of continuous probability distributions and play important roles in statistical theory. A Generalised Exponential-Lindley Distribution (GELD) was given by Mishra and Sah (2015) of which, both the exponential and the Lindley distributions are the particular cases. Mixtures of distributions form an important class of distributions in the domain of probability distributions. A mixture distribution arises when some or all the parameters in a probability function vary according to certain probability law. In this paper, a Generalised Exponential- Lindley Mixture of Poisson Distribution (GELMPD) has been obtained by mixing Poisson distribution with the GELD. Materials and Methods: It is based on the concept of the generalisations of some continuous mixtures of Poisson distribution. Results: The Probability mass of function of generalized exponential-Lindley mixture of Poisson distribution has been obtained by mixing Poisson distribution with GELD. The first four moments about origin of this distribution have been obtained. The estimation of its parameters has been discussed using method of moments and also as maximum likelihood method. This distribution has been fitted to a number of discrete data-sets which are negative binomial in nature and it has been observed that the distribution gives a better fit than the Poisson–Lindley Distribution (PLD) of Sankaran (1970). Conclusion: P-value of the GELMPD is found greater than that in case of PLD. Hence, it is expected to be a better alternative to the PLD of Sankaran for similar type of discrete data-set which is negative binomial in nature.

scholarly journals Weighted Negative Binomial Poisson-Lindley Distribution with Actuarial Applications

2018 ◽  
Author(s):  
Hossein Zamani ◽  
Noriszura Ismail ◽  
Marzieh Shekari
Keyword(s):  
Maximum Likelihood Method ◽  
Negative Binomial ◽  
Statistical Tests ◽  
Discrete Distribution ◽  
Likelihood Method ◽  
Weighted Version ◽  
Lindley Distribution ◽  
Weighted Distribution ◽  
Binomial Distributions ◽  
Over Dispersion

This study introduces a new discrete distribution which is a weighted version of Poisson-Lindley distribution. The weighted distribution is obtained using the negative binomial weight function and can be fitted to count data with over-dispersion. The p.m.f., p.g.f. and simulation procedure of the new weighted distribution, namely weighted negative binomial Poisson-Lindley (WNBPL), are provided. The maximum likelihood method for parameter estimation is also presented. The WNBPL distribution is fitted to several insurance datasets, and is compared to the Poisson and negative binomial distributions in terms of several statistical tests.

scholarly journals Characterizations of Twenty (2020-2021) Proposed Discrete Distributions

2021 ◽  
pp. 847-884
Author(s):  
G.G. Hamedani ◽  
Mahrokh Najaf ◽  
Amin Roshani ◽  
Nadeem Shafique Butt
Keyword(s):  
Exponential Distribution ◽  
Poisson Distribution ◽  
Geometric Distribution ◽  
Discrete Distribution ◽  
Gumbel Distribution ◽  
Rayleigh Distribution ◽  
Discrete Distributions ◽  
Lindley Distribution ◽  
Lomax Distribution ◽  
Two Parameter

In this paper, certain characterizations of twenty newly proposed discrete distributions: the discrete gen- eralized Lindley distribution of El-Morshedy et al.(2021), the discrete Gumbel distribution of Chakraborty et al.(2020), the skewed geometric distribution of Ong et al.(2020), the discrete Poisson X gamma distri- bution of Para et al.(2020), the discrete Cos-Poisson distribution of Bakouch et al.(2021), the size biased Poisson Ailamujia distribution of Dar and Para(2021), the generalized Hermite-Genocchi distribution of El-Desouky et al.(2021), the Poisson quasi-xgamma distribution of Altun et al.(2021a), the exponentiated discrete inverse Rayleigh distribution of Mashhadzadeh and MirMostafaee(2020), the Mlynar distribution of Fr¨uhwirth et al.(2021), the flexible one-parameter discrete distribution of Eliwa and El-Morshedy(2021), the two-parameter discrete Perks distribution of Tyagi et al.(2020), the discrete Weibull G family distribution of Ibrahim et al.(2021), the discrete Marshall–Olkin Lomax distribution of Ibrahim and Almetwally(2021), the two-parameter exponentiated discrete Lindley distribution of El-Morshedy et al.(2019), the natural discrete one-parameter polynomial exponential distribution of Mukherjee et al.(2020), the zero-truncated discrete Akash distribution of Sium and Shanker(2020), the two-parameter quasi Poisson-Aradhana distribution of Shanker and Shukla(2020), the zero-truncated Poisson-Ishita distribution of Shukla et al.(2020) and the Poisson-Shukla distribution of Shukla and Shanker(2020) are presented to complete, in some way, the au- thors’ works.

Generalized Hypergeometric Factorial Moment Distribution of Order k

2000 ◽  
Vol 50 (1-2) ◽  
pp. 71-78 ◽  
Author(s):  
C. Satheesh Kumar ◽  
T. S. K. Moothathu
Keyword(s):  
Negative Binomial ◽  
Factorial Moment ◽  
Mass Function ◽  
Discrete Distributions ◽  
Probability Mass Function ◽  
Factorial Moments ◽  
Point Distribution ◽  
Moment Distribution ◽  
Special Cases ◽  
Probability Mass

Here we introduce the generalized hypergeometric functional moment distribution of order k (GHFMD (k)) in the distribution of the random sum [Formula: see text] having Hira no's k-point distribution, where N, independent of X j's, has the generalized hypergeomet ric factorial moment distribution. Well-known discrete distributions of order k such as cluster binomial, cluster negative binomial and extended Poisson are shown to be special cases of GHFMD(k). The probability mass function, recurrence relations for probabilities and factorial moments of GHFMD (k) are found out. The beta or the gamma mixture of GHFMD (k) is shown to be a GHFMD (k). Finally GHFMD (k) is obtained as a limit of another GHFMD (k). AMS (2000) Subject Classification: Primary 60E05, 60E10; Secondary 33C20.

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 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).

Sign in / Sign up

Export Citation Format

Share Document