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 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 COMPARATIVE STUDY BETWEEN TWO DISCRETE LINDLEY DISTRIBUTIONS

2017 ◽  
Vol 39 (3) ◽  
pp. 539 ◽  
Author(s):  
Ricardo Puziol Oliveira ◽  
Josmar Mazucheli ◽  
Jorge Alberto Achcar
Keyword(s):  
Maximum Likelihood ◽  
Infinite Series ◽  
Probability Function ◽  
Negative Binomial ◽  
Mean Squared Error ◽  
Real Data ◽  
Bias Reduction ◽  
Lindley Distribution ◽  
Binomial Distributions ◽  
Squared Error

The methods of generate a probability function from a probability density function has long been used in recent years. In general, the discretization process produces probability functions that can be rivals to traditional distributions used in the analysis of count data as the geometric, the Poisson and negative binomial distributions. In this paper, by the method based on an infinite series, we studied an alternative discrete Lindley distribution to those study in Gomez (2011) and Bakouch (2014). For both distributions, a simulation study is carried out to examine the bias and mean squared error of the maximum likelihood estimators of the parameters as well as the coverage probability and the width of the confidence intervals. For the discrete Lindley distribution obtained by infinite series method we present the analytical expression for bias reduction of the maximum likelihood estimator. Some examples using real data from the literature show the potential of these distributions. 

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.

Zero-truncated Poisson-Lindley distribution

2021 ◽  
pp. 40-50
Author(s):  
Afida Nurul Hilma ◽  
Dian Lestari ◽  
Sindy Devila
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Likelihood Method ◽  
Lindley Distribution ◽  
Count Distribution ◽  
Distribution Parameters ◽  
Counting Distribution ◽  
Over Dispersion

In order to find a counting distribution that can handle the condition when the data has no zero-count. Distribution named Zero-truncated Poisson-Lindley distribution is developed. It can handle the condition when the data has no zero-count both in over-dispersion and under-dispersion. In this paper, characteristics of Zero-truncated Poisson-Lindley distribution are obtained and estimate distribution parameters using the maximum likelihood method. Then, the application of the model to real data is given.

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 Odd Lomax-Kumaraswamy Distribution: Its Properties and Applications

2020 ◽  
pp. 45-60
Author(s):  
Bassa Shiwaye Yakura ◽  
Ahmed Askira Sule ◽  
Mustapha Mohammed Dewu ◽  
Kabiru Ahmed Manju ◽  
Fadimatu Bawuro Mohammed
Keyword(s):  
Goodness Of Fit ◽  
Real Data ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Distribution Functions ◽  
Model Parameters ◽  
Data Sets ◽  
Kumaraswamy Distribution ◽  
Method Of Maximum Likelihood ◽  
Family Of Distributions

This article uses the odd Lomax-G family of distributions to study a new extension of the Kumaraswamy distribution called “odd Lomax-Kumaraswamy distribution”. In this article, the density and distribution functions of the odd Lomax-Kumaraswamy distribution are defined and studied with many other properties of the distribution such as the ordinary moments, moment generating function, characteristic function, quantile function, reliability functions, order statistics and other useful measures. The model parameters are estimated by the method of maximum likelihood. The goodness-of-fit of the proposed distribution is demonstrated using two real data sets.

scholarly journals On Erlang-Truncated Exponential Distribution: Theory and Application

2021 ◽  
pp. 155-168
Author(s):  
Ibrahim Elbatal ◽  
A. Aldukeel
Keyword(s):  
Exponential Distribution ◽  
Real Data ◽  
Moment Generating Function ◽  
Likelihood Method ◽  
Mean Deviation ◽  
Model Parameters ◽  
Data Sets ◽  
Survival Times ◽  
New Distribution ◽  
Better Than

In this article, we introduce a new distribution called the McDonald Erlangtruncated exponential distribution. Various structural properties including explicit expressions for the moments, moment generating function, mean deviation of the new distribution are derived. The estimation of the model parameters is performed by maximum likelihood method. The usefulness of the new distribution is illustrated by two real data sets. The new model is much better than other important competitive models in modeling relief times and survival times data sets.

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 A New Generalized Weighted Weibull Distribution

2019 ◽  
pp. 161-178 ◽  
Author(s):  
Salman Abbas ◽  
Gamze Ozal ◽  
Saman Hanif Shahbaz ◽  
Muhammad Qaiser Shahbaz
Keyword(s):  
Weibull Distribution ◽  
Generating Function ◽  
Probability Generating Function ◽  
Real Data ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
Proposed Model

In this article, we present a new generalization of weighted Weibull distribution using Topp Leone family of distributions. We have studied some statistical properties of the proposed distribution including quantile function, moment generating function, probability generating function, raw moments, incomplete moments, probability, weighted moments, Rayeni and q th entropy. The have obtained numerical values of the various measures to see the eect of model parameters. Distribution of of order statistics for the proposed model has also been obtained. The estimation of the model parameters has been done by using maximum likelihood method. The eectiveness of proposed model is analyzed by means of a real data sets. Finally, some concluding remarks are given.

scholarly journals The Exponentiated Burr–Hatke Distribution and Its Discrete Version: Reliability Properties with CSALT Model, Inference and Applications

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2277
Author(s):  
Mahmoud El-Morshedy ◽  
Hassan M. Aljohani ◽  
Mohamed S. Eliwa ◽  
Mazen Nassar ◽  
Mohammed K. Shakhatreh ◽  
...  
Keyword(s):  
Hazard Rate ◽  
Real Life ◽  
Real Data ◽  
Rate Function ◽  
Discrete Analog ◽  
Discrete Distributions ◽  
Discrete Version ◽  
Continuous Version ◽  
Data Set ◽  
Accelerated Life Tests

Continuous and discrete distributions are essential to model both continuous and discrete lifetime data in several applied sciences. This article introduces two extended versions of the Burr–Hatke model to improve its applicability. The first continuous version is called the exponentiated Burr–Hatke (EBuH) distribution. We also propose a new discrete analog, namely the discrete exponentiated Burr–Hatke (DEBuH) distribution. The probability density and the hazard rate functions exhibit decreasing or upside-down shapes, whereas the reversed hazard rate function. Some statistical and reliability properties of the EBuH distribution are calculated. The EBuH parameters are estimated using some classical estimation techniques. The simulation results are conducted to explore the behavior of the proposed estimators for small and large samples. The applicability of the EBuH and DEBuH models is studied using two real-life data sets. Moreover, the maximum likelihood approach is adopted to estimate the parameters of the EBuH distribution under constant-stress accelerated life-tests (CSALTs). Furthermore, a real data set is analyzed to validate our results under the CSALT model.

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