scholarly journals A DISCRETE ANALOGUE OF THE CONTINUOUS POWER LINDLEY DISTRIBUTION AND ITS APPLICATIONS

2018 ◽  
Vol 36 (3) ◽  
pp. 649 ◽  
Author(s):  
Ricardo Puziol OLIVEIRA ◽  
Josmar MAZUCHELI ◽  
Márcia Lorena Alves SANTOS ◽  
Kelly Vanessa Parede BARCO
Keyword(s):  
Maximum Likelihood ◽  
Probability Distributions ◽  
Survival Function ◽  
Continuous Distribution ◽  
Discrete Analogue ◽  
Discrete Models ◽  
Lindley Distribution ◽  
Power Lindley Distribution ◽  
Proposed Model ◽  
Continuous Power

Methods to generate a discrete analogue of a continuous distribution have been widely considered in recent decades. In general, the discretization procedure comprises in transform continuous attributes into discrete attributes generating new probability distributions that could be an alternative to the traditional  discrete models, such as Poisson and Binomial models, commonly used in analysis of count data. It also  avoids the use of continuous in the analysis of strictly discrete data. In this paper, using the discretization  method based on the survival function, it is introduced a discrete analogue of power Lindley distribution. Some mathematical properties are studied. The maximum likelihood theory is considered for estimation and asymptotic inference concerns. A simulation study is also carried out in order to evaluate some properties of the maximum likelihood estimators of the proposed model. The usefulness and accurate of the proposed model are evaluated using real datasets provided by the literature.

scholarly journals Discrete Gompertz-G Family of Distributions for Over- and Under-Dispersed Data with Properties, Estimation, and Applications

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 358 ◽  
Author(s):  
M. S. Eliwa ◽  
Ziyad Ali Alhussain ◽  
M. El-Morshedy
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Discrete Analogue ◽  
Likelihood Method ◽  
New Family ◽  
Distributional Properties ◽  
Reliability Characteristics ◽  
Proposed Model ◽  
The Family ◽  
Family Of Distributions

Alizadeh et al. introduced a flexible family of distributions, in the so-called Gompertz-G family. In this article, a discrete analogue of the Gompertz-G family is proposed. We also study some of its distributional properties and reliability characteristics. After introducing the general class, three special models of the new family are discussed in detail. The maximum likelihood method is used for estimating the family parameters. A simulation study is carried out to assess the performance of the family parameters. Finally, the flexibility of the new family is illustrated by means of four genuine datasets, and it is found that the proposed model provides a better fit than the competitive distributions.

scholarly journals Modified Slash Lindley Distribution

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Jimmy Reyes ◽  
Osvaldo Venegas ◽  
Héctor W. Gómez
Keyword(s):  
Maximum Likelihood ◽  
Simulation Study ◽  
Maximum Likelihood Estimators ◽  
Lindley Distribution ◽  
Basic Properties ◽  
Moment Estimators ◽  
Proposed Model ◽  
Distribution Moment ◽  
Flexible Models ◽  
New Distribution

In this paper we introduce a new distribution, called the modified slash Lindley distribution, which can be seen as an extension of the Lindley distribution. We show that this new distribution provides more flexibility in terms of kurtosis and skewness than the Lindley distribution. We derive moments and some basic properties for the new distribution. Moment estimators and maximum likelihood estimators are calculated using numerical procedures. We carry out a simulation study for the maximum likelihood estimators. A fit of the proposed model indicates good performance when compared with other less flexible models.

scholarly journals A Weibull-Gompertz Makeham Distribution with Properties and Application to Cancer Data

2019 ◽  
pp. 1-17
Author(s):  
Peter O. Koleoso ◽  
Angela U. Chukwu
Keyword(s):  
Bladder Cancer ◽  
Maximum Likelihood ◽  
Order Statistics ◽  
Hazard Function ◽  
Probability Distributions ◽  
Survival Function ◽  
Statistical Properties ◽  
Cancer Data ◽  
Method Of Maximum Likelihood ◽  
Flexible Model

The article presents an extension of the Gompertz Makeham distribution using the Weibull-G family of continuous probability distributions proposed by Tahir et al. (2016a). This new extension generates a more flexible model called Weibull-Gompertz Makeham distribution. Some statistical properties of the distribution which include the moments, survival function, hazard function and distribution of order statistics were derived and discussed. The parameters were estimated by the method of maximum likelihood and the distribution was applied to a bladder cancer data. Weibull-Gompertz Makeham distribution performed best (AIC = -6.8677, CAIC = -6.3759, BIC = 7.3924) when compared with other existing distributions of the same family to model bladder cancer data.

scholarly journals Estimation a Stress-Strength Model for P (Yr:n1 < Xk:n2 ) Using the Lindley Distribution

2017 ◽  
Vol 40 (1) ◽  
pp. 105-121 ◽  
Author(s):  
Marwa Khalil
Keyword(s):  
Maximum Likelihood ◽  
Simulation Study ◽  
Real Data ◽  
Minimum Variance ◽  
Strength Model ◽  
Practical Application ◽  
Likelihood Estimator ◽  
Lindley Distribution ◽  
Minimum Variance Unbiased Estimator ◽  
Proposed Model

The problem of estimation reliability in a multicomponent stress-strength model, when the system consists of k components have strength each compo- nent experiencing a random stress, is considered in this paper. The reliability of such a system is obtained when strength and stress variables are given by Lindley distribution. The system is regarded as alive only if at least r out of k (r < k) strength exceeds the stress. The multicomponent reliability of the system is given by Rr,k . The maximum likelihood estimator (M LE), uniformly minimum variance unbiased estimator (UMVUE) and Bayes esti- mator of Rr,k are obtained. A simulation study is performed to compare the different estimators of Rr,k . Real data is used as a practical application of the proposed model.

Marshall-Olkin Extended Power Lindley Distribution with Application

2018 ◽  
Vol 2 (2) ◽  
pp. 84
Author(s):  
Rafif Hibatullah ◽  
Yekti Widyaningsih ◽  
Sarini Abdullah
Keyword(s):  
Density Function ◽  
Model Comparison ◽  
Scale Parameter ◽  
Survival Function ◽  
Weibull Model ◽  
Cumulative Distribution ◽  
Likelihood Method ◽  
Lindley Distribution ◽  
Power Lindley Distribution ◽  
Extended Power

Lindley distribution was introduced by Lindley (1958) in the context of Bayes inference. Its density function is obtained by mixing the exponential distribution, with scale parameter β, and the gamma distribution, with shape parameter 2 and scale parameter β. Recently, a new generalization of the Lindley distribution was proposed by Ghitany et al. (2013), called power Lindley distribution. This paper will introduce an extension of the power Lindley distribution using the Marshall-Olkin method, resulting in Marshall-Olkin Extended Power Lindley (MOEPL) distribution. The MOEPL distribution offers a flexibility in representing data with various shapes. This flexibility is due to the addition of a parameter to the power Lindley distribution. Some properties of the MOEPL were explored, such as probability density function (pdf), cumulative distribution function (cdf), hazard rate, survival function, quantiles, and moments. Estimation of the MOEPL parameters was conducted using maximum likelihood method. The proposed distribution was applied to data. The results were given which illustrate the MOEPL distribution and were compared to Lindley, power Lindley, gamma, and Weibull. Model comparison using the log likelihood, AIC, and BIC showed that MOEPL fit the data better than the other distributions.

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 the Alpha Power Transformed Power Lindley Distribution

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Amal S. Hassan ◽  
M. Elgarhy ◽  
Rokaya E. Mohamd ◽  
Sharifah Alrajhi
Keyword(s):  
Weighted Least Squares ◽  
Stochastic Ordering ◽  
Data Sets ◽  
Alpha Power ◽  
Population Parameters ◽  
Important Data ◽  
Lindley Distribution ◽  
Power Lindley Distribution ◽  
Proposed Model ◽  
Extensive Numerical Simulation

In this paper, we introduce a new generalization of the power Lindley distribution referred to as the alpha power transformed power Lindley (APTPL). The APTPL model provides a better fit than the power Lindley distribution. It includes the alpha power transformed Lindley, power Lindley, Lindley, and gamma as special submodels. Various properties of the APTPL distribution including moments, incomplete moments, quantiles, entropy, and stochastic ordering are obtained. Maximum likelihood, maximum products of spacings, and ordinary and weighted least squares methods of estimation are utilized to obtain the estimators of the population parameters. Extensive numerical simulation is performed to examine and compare the performance of different estimates. Two important data sets are employed to show how the proposed model works in practice.

scholarly journals Bayesian and non-Bayesian estimation of four-parameter of bivariate discrete inverse Weibull distribution with applications to model failure times, football and biological data

Filomat ◽  
2020 ◽  
Vol 34 (8) ◽  
pp. 2511-2531 ◽  
Author(s):  
M.S. Eliwa ◽  
M. El-Morshedy
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Real Data ◽  
Discrete Analogue ◽  
Biological Data ◽  
Model Parameters ◽  
Data Sets ◽  
Proposed Model ◽  
Inverse Weibull Distribution ◽  
Detailed Simulation

In this paper we have considered one model, namely the bivariate discrete inverse Weibull distribution, which has not been considered in the statistical literature yet. The proposed model is a discrete analogue of Marshall-Olkin inverse Weibull distribution. Some of its important statistical properties are studied. Maximum likelihood and Bayesian methods are used to estimate the model parameters. A detailed simulation study is carried out to examine the bias and mean square error of maximum likelihood and Bayesian estimators. Finally, three real data sets are analyzed to illustrate the importance of the proposedmodel.

scholarly journals Uma proposta para identificação de outliers multivariados

2018 ◽  
Vol 40 ◽  
pp. 40
Author(s):  
Josino José Barbosa ◽  
Tiago Martins Pereira ◽  
Fernando Luiz Pereira de Oliveira
Keyword(s):  
Probability Distributions ◽  
Estimation Method ◽  
Real Data ◽  
Cumulative Distribution ◽  
Likelihood Method ◽  
Inverse Power ◽  
Test Statistic ◽  
Lindley Distribution ◽  
Power Lindley Distribution ◽  
Inverse Lindley Distribution

In the last years several probability distributions have been proposed in the literature, especially with the aim of obtaining models that are more flexible relative to the behaviors of the density and hazard rate functions. For instance, Ghitany et al. (2013) proposed a new generalization of the Lindley distribution, called power Lindley distribution, whereas Sharma et al. (2015a) proposed the inverse Lindley distribution. From these two generalizations Barco et al. (2017) studied the inverse power Lindley distribution, also called by Sharma et al. (2015b) as generalized inverse Lindley distribution. Considering the inverse power Lindley distribution, in this paper is evaluate the performance, through Monte Carlo simulations, with respect to the bias and consistency of nine different methods of estimations (the maximum likelihood method and eight others based on the distance between the empirical and theoretical cumulative distribution function). The numerical results showed a better performance of the estimation method based on the Anderson-Darling test statistic. This conclusion is also observed in the analysis of two real data sets.

scholarly journals The Extended Marshall-Olkin Burr III Distribution: Properties and Applications

2021 ◽  
pp. 1-14
Author(s):  
Muhammad Ahsan ul Haq ◽  
Ahmed Z. Afify ◽  
Hazem Al- Mofleh ◽  
Rana Muhammad Usman ◽  
Mohammed Alqawba ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Density Function ◽  
Continuous Distribution ◽  
Real Data ◽  
Model Parameters ◽  
Data Set ◽  
Mathematical Properties ◽  
Proposed Model ◽  
Method Of Maximum Likelihood ◽  
Burr Iii Distribution

We study a new continuous distribution called the Marshall-Olkin modified Burr III distribution. The density function of the proposed model can be expressed as a mixture of modified Burr III densities. A comprehensive account of its mathematical properties is derived. The model parameters are estimated by the method of maximum likelihood. The usefulness of the derived model is illustrated over other distributions using a real data set.

Sign in / Sign up

Export Citation Format

Share Document