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 Alpha Power Transformed Lindley Distribution

2021 ◽  
pp. 130-142
Author(s):  
L A Rosa ◽  
S Nurrohmah ◽  
I Fithriani
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Hazard Rate ◽  
Survival Function ◽  
Cumulative Distribution ◽  
Likelihood Method ◽  
Alpha Power ◽  
Lindley Distribution ◽  
Modelling Data

The one parameter Lindley distribustion (theta) has been widely used in various field such as biology, technique, medical, and industries. Lindley distribution is capable for modelling data with monotone increasing hazard rate. However, in real life, there are situations where the hazard rate is not monotone. Therefore, to enhance the Lindley distribution capabilitiesfor modelling data, a modification can be used by using Alpha Power Transformed method. The result of the modification of Lindley distribution is commonly called Alpha Power Transformed Lindley distribution (APTL) distribution that has two parameters (alpha, theta). This new APTL distribution is appropriate in modelling data with decreasing or unimodal shaped of probability density function, and has hazard rates with increasing, decreasing, and upside-down bathtub shaped. The properties of the proposed distribution are discussed include probability density function, cumulative distribution function, survival function, hazard rate function, moment generating function, and rth moment. Themodel parameters are obtained using maximum likelihood method. The waiting time data is used as an illustration to describe the utility of APTL distribution.

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 On a new distribution based on the arccosine function

2021 ◽  
Author(s):  
Christophe Chesneau ◽  
Lishamol Tomy ◽  
Jiju Gillariose
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Hazard Rate ◽  
Survival Function ◽  
Real Data ◽  
Cumulative Distribution ◽  
Data Sets ◽  
Power Functions ◽  
New Distribution

AbstractThis note focuses on a new one-parameter unit probability distribution centered around the inverse cosine and power functions. A special case of this distribution has the exact inverse cosine function as a probability density function. To our knowledge, despite obvious mathematical interest, such a probability density function has never been considered in Probability and Statistics. Here, we fill this gap by pointing out the main properties of the proposed distribution, from both the theoretical and practical aspects. Specifically, we provide the analytical form expressions for its cumulative distribution function, survival function, hazard rate function, raw moments and incomplete moments. The asymptotes and shape properties of the probability density and hazard rate functions are described, as well as the skewness and kurtosis properties, revealing the flexible nature of the new distribution. In particular, it appears to be “round mesokurtic” and “left skewed”. With these features in mind, special attention is given to find empirical applications of the new distribution to real data sets. Accordingly, the proposed distribution is compared with the well-known power distribution by means of two real data sets.

scholarly journals An Extended Power Lindley Distribution and its Application

2016 ◽  
Vol 11 (2) ◽  
pp. 1075-1094
Author(s):  
Ibrahim Elbatal ◽  
Yehia Mousa El Gebaly ◽  
Essam Ali Amin
Keyword(s):  
Lindley Distribution ◽  
Power Lindley Distribution ◽  
Extended Power

scholarly journals The Generalized Ampadu-G Family of Distributions: Properties, Applications and Characterizations

2020 ◽  
pp. 139-167
Author(s):  
Clement Boateng Ampadu ◽  
Abdulzeid Yen Anafo
Keyword(s):  
Weibull Distribution ◽  
Density Function ◽  
Survival Function ◽  
Real Life ◽  
Life Time ◽  
Quantile Function ◽  
Cumulative Distribution ◽  
Model Parameters ◽  
New Family ◽  
Family Of Distributions

This paper introduces a new class of distributions called the generalized Ampadu-G (GA-G for short) family of distributions, and with a certain restriction on the parameter space, the family is shown to be a life-time distribution. The shape of the density function and hazard rate function of the GA-G family is described analytically. When G follows the Weibull distribution, the generalized Ampadu-Weibull (GA-W for short) is presented along with its hazard and survival function. Several sub-models of the GA-W family are presented. The transformation technique is applied to this new family of distributions, and we obtain the quantile function of the new family. Power series representations for the cumulative distribution function (CDF) and probability density function (PDF) are also obtained. The rth non-central moments, moment generating function, and Renyi entropy associated with the new family of distributions are derived. Characterization theorems based on two truncated moments and conditional expectation are also presented. A simulation study is also conducted, and we find that using the method of maximum likelihood to estimate model parameters is adequate. The GA-W family of distributions is shown to be practically significant in modeling real life data, and is shown to be superior to some non-trivial generalizations of the Weibull distribution. A further development concludes the paper.

scholarly journals A New Generalized Poisson-Lindley Distribution: Applications and Properties

2015 ◽  
Vol 44 (4) ◽  
pp. 35-51 ◽  
Author(s):  
Deepesh Bhati ◽  
DVS Sastry ◽  
PZ Maha Qadri
Keyword(s):  
Risk Model ◽  
Cumulative Distribution ◽  
Likelihood Method ◽  
Lindley Distribution ◽  
Generalized Poisson ◽  
Collective Risk Model ◽  
Collective Risk ◽  
Competing Models ◽  
Secondary Distribution ◽  
Better Than

A new generalized Poisson Lindley distribution is obtained by compounding Poissondistribution with two parameter generalised Lindley distribution. The new distribution isshown to be unimodal and over dispersed. This distribution has a tendency to accommodate right tail as well as for particular values of parameter the tail tends to zero at a faster rate. Various properties like cumulative distribution function, generating function, Moments etc. are derived. Knowledge about the parameters is obtained through Method of Moments, Maximum Likelihood Method and EM Algorithm. Moreover, an actuarial application in collective risk model is shown by considering the proposed distribution as primary and Exponential and Erlang as secondary distribution. The model is applied to real dataset and found to perform better than competing models.

scholarly journals Estimation of Survival Function for Rayleigh Distribution by Ranking function:-

2019 ◽  
Vol 16 (3(Suppl.)) ◽  
pp. 0775
Author(s):  
Hussein Et al.
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Scale Parameter ◽  
Survival Function ◽  
Rayleigh Distribution ◽  
Ordinary Least Squares ◽  
Ranking Functions ◽  
Hazard Functions ◽  
Ordinary Least Squares Estimator

In this article, performing and deriving te probability density function for Rayleigh distribution is done by using ordinary least squares estimator method and Rank set estimator method. Then creating interval for scale parameter of Rayleigh distribution. Anew method using   is used for fuzzy scale parameter. After that creating the survival and hazard functions for two ranking functions are conducted to show which one is beast.

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.

Sign in / Sign up

Export Citation Format

Share Document