The Reflected-Shifted-Truncated Lindley Distribution with Applications

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Sanku Dey ◽  
Sophia Waymyers ◽  
Devendra Kumar
Keyword(s):  
Maximum Likelihood ◽  
Censored Data ◽  
Real Data ◽  
Comprehensive Treatment ◽  
Model Parameters ◽  
Data Sets ◽  
Right Censored Data ◽  
Lindley Distribution ◽  
Failure Data ◽  
Maximum Likelihood Methods

AbstractIn this paper, a new probability density function with bounded domain is presented. The new distribution arises from the Lindley distribution proposed in 1958. It presents the advantage of not including any special function in its formulation. The new transformed model, called the reflected-shifted-truncated Lindley distribution can be used to model left-skewed data. We provide a comprehensive treatment of general mathematical and statistical properties of this distribution. We estimate the model parameters by maximum likelihood methods based on complete and right-censored data. To assess the performance and consistency of the maximum likelihood estimators, we conduct a simulation study with varying sample sizes. Finally, we use the distribution to model left-skewed survival and failure data from two real data sets. For the real data sets containing complete data and right-censored data, this distribution is superior in its ability to sufficiently model the data as compared to the power Lindley, exponentiated power Lindley, generalized inverse Lindley, generalized weighted Lindley and the well-known Gompertz distributions.

scholarly journals Beta Kumaraswamy Burr Type X Distribution and Its Properties

2018 ◽  
Author(s):  
Umar Yusuf Madaki ◽  
Mohd Rizam Abu Bakar ◽  
Laba Handique
Keyword(s):  
Maximum Likelihood ◽  
Reliability Analysis ◽  
Real Data ◽  
Quantile Function ◽  
Model Parameters ◽  
Data Sets ◽  
Likelihood Methods ◽  
Proposed Model ◽  
Maximum Likelihood Methods ◽  
True Values

We proposed a so-called Beta Kumaraswamy Burr Type X distribution which gives the extension of the Kumaraswamy-G class of family distribution. Some properties of this proposed model were provided, like: the expansion of densities and quantile function. We considered the Bayes and maximum likelihood methods to estimate the parameters and also simulate the model parameters to validate the methods based on different set of true values. Some real data sets were employed to show the usefulness and flexibility of the model which serves as generalization to many sub-models in the field of engineering, medical, survival and reliability analysis.

scholarly journals Beta Kumaraswamy Burr Type X Distribution and Its Properties

2018 ◽  
Author(s):  
Umar Yusuf Madaki ◽  
Mohd Rizam Abu Bakar ◽  
Laba Handique
Keyword(s):  
Maximum Likelihood ◽  
Reliability Analysis ◽  
Real Data ◽  
Quantile Function ◽  
Model Parameters ◽  
Data Sets ◽  
Likelihood Methods ◽  
Proposed Model ◽  
Maximum Likelihood Methods ◽  
True Values

We proposed a so-called Beta Kumaraswamy Burr Type X distribution which gives the extension of the Kumaraswamy-G class of family distribution. Some properties of this proposed model were provided, like: the expansion of densi- ties and quantile function. We considered the Bayes and maximum likelihood methods to estimate the parameters and also simulate the model parameters to validate the methods based on dierent set of true values. Some real data sets were employed to show the usefulness and  exibility of the model which serves as generalization to many sub-models in the elds of engineering, medical, survival and reliability analysis.

scholarly journals Classical and Bayesian inference approaches for the exponentiated discrete Weibull model with censored data and a cure fraction

2021 ◽  
pp. 467-481
Author(s):  
Jorge Alberto Achcar ◽  
Edson Zangiacomi Martinez ◽  
Bruno Caparroz Lopes de Freitas ◽  
Marcos Vinicius de Oliveira Peres
Keyword(s):  
Maximum Likelihood ◽  
Censored Data ◽  
Likelihood Estimation ◽  
Real Data ◽  
Weibull Model ◽  
Data Sets ◽  
Right Censored Data ◽  
Extensive Simulation ◽  
Proposed Model ◽  
Cure Fraction

In this paper, we introduce maximum likelihood and Bayesian parameter estimation for the exponentiated discrete Weibull (EDW) distribution in presence of randomly right censored data. We also consider the inclusion of a cure fraction in the model. The performance of the maximum likelihood estimation approach is assessed by conducting an extensive simulation study with different sample sizes and different values for the parameters of the EDW distribution. The usefuness of the proposed model is illustrated with two examples considering real data sets.

scholarly journals The Weibull Birnbaum-Saunders Distribution And Its Applications

2020 ◽  
Vol 9 (1) ◽  
pp. 61-81
Author(s):  
Lazhar BENKHELIFA
Keyword(s):  
Maximum Likelihood ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Reliability Estimation ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Data Sets ◽  
Proposed Model ◽  
Modeling Data

A new lifetime model, with four positive parameters, called the Weibull Birnbaum-Saunders distribution is proposed. The proposed model extends the Birnbaum-Saunders distribution and provides great flexibility in modeling data in practice. Some mathematical properties of the new distribution are obtained including expansions for the cumulative and density functions, moments, generating function, mean deviations, order statistics and reliability. Estimation of the model parameters is carried out by the maximum likelihood estimation method. A simulation study is presented to show the performance of the maximum likelihood estimates of the model parameters. The flexibility of the new model is examined by applying it to two real data sets.

scholarly journals A New Flexible Three-Parameter Model: Properties, Clayton Copula, and Modeling Real Data

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 440 ◽  
Author(s):  
Abdulhakim A. Al-babtain ◽  
I. Elbatal ◽  
Haitham M. Yousof
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Likelihood Method ◽  
Model Parameters ◽  
Simple Type ◽  
Data Sets ◽  
New Model ◽  
Clayton Copula ◽  
Mathematical Properties

In this article, we introduced a new extension of the binomial-exponential 2 distribution. We discussed some of its structural mathematical properties. A simple type Copula-based construction is also presented to construct the bivariate- and multivariate-type distributions. We estimated the model parameters via the maximum likelihood method. Finally, we illustrated the importance of the new model by the study of two real data applications to show the flexibility and potentiality of the new model in modeling skewed and symmetric data sets.

scholarly journals JMASM 51: Bayesian Reliability Analysis of Binomial Model – Application to Success/Failure Data

2019 ◽  
Vol 17 (2) ◽  
Author(s):  
M. Tanwir Akhtar ◽  
Athar Ali Khan
Keyword(s):  
Bayesian Model ◽  
Real Data ◽  
Model Parameters ◽  
Data Sets ◽  
Binomial Model ◽  
Model Application ◽  
Simulation Tools ◽  
Failure Data ◽  
Simulation Techniques ◽  
Bayesian Paradigm

Reliability data are generated in the form of success/failure. An attempt was made to model such type of data using binomial distribution in the Bayesian paradigm. For fitting the Bayesian model both analytic and simulation techniques are used. Laplace approximation was implemented for approximating posterior densities of the model parameters. Parallel simulation tools were implemented with an extensive use of R and JAGS. R and JAGS code are developed and provided. Real data sets are used for the purpose of illustration.

scholarly journals A Reliability Model Based on the Incomplete Generalized Integro-Exponential Function

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1537
Author(s):  
Juan M. Astorga ◽  
Jimmy Reyes ◽  
Karol I. Santoro ◽  
Osvaldo Venegas ◽  
Héctor W. Gómez
Keyword(s):  
Maximum Likelihood ◽  
Exponential Function ◽  
Real Data ◽  
Data Sets ◽  
Reliability Model ◽  
Likelihood Methods ◽  
Parameter Recovery ◽  
High Coefficient ◽  
Positive Data ◽  
Maximum Likelihood Methods

This article introduces an extension of the Power Muth (PM) distribution for modeling positive data sets with a high coefficient of kurtosis. The resulting distribution has greater kurtosis than the PM distribution. We show that the density can be represented based on the incomplete generalized integro-exponential function. We study some of its properties and moments, and its coefficients of asymmetry and kurtosis. We apply estimations using the moments and maximum likelihood methods and present a simulation study to illustrate parameter recovery. The results of application to two real data sets indicate that the new model performs very well in the presence of outliers.

scholarly journals A Non-Mixture Cure Model for Right Censored Data with Fréchet Distribution

2018 ◽  
Author(s):  
Durga Kutal ◽  
Lianfen Qian
Keyword(s):  
Censored Data ◽  
Real Data ◽  
Phase Iii ◽  
Likelihood Method ◽  
Model Parameters ◽  
Exponential Distributions ◽  
Right Censored Data ◽  
Cure Model ◽  
Mixture Cure Model ◽  
Allogeneic Marrow

This paper considers a non-mixture cure model for right censored data. It utilizes the maximum likelihood method to estimate model parameters in the non-mixture cure model. The simulation study is based on Fréchet susceptible distribution to evaluate the performance of the method. Comparing with Weibull and exponentiated exponential distributions, the non-mixture Fréchet distribution is shown to be the best in modeling a real data on allogeneic marrow HLA-matched donors and ECOG phase III clinical trial e1684 data.

scholarly journals Generalized Weighted Rama Distribution: Properties and Application to Model Lifetime Data

2021 ◽  
pp. 9-37
Author(s):  
Samuel U. Enogwe ◽  
Chisimkwuo John ◽  
Happiness O. Obiora-Ilouno ◽  
Chrisogonus K. Onyekwere
Keyword(s):  
Maximum Likelihood ◽  
Likelihood Estimation ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Data Sets ◽  
Estimation Of Parameters ◽  
Data Set ◽  
Bathtub Shape ◽  
Asymptotic Confidence Intervals

In this paper, we propose a new lifetime distribution called the generalized weighted Rama (GWR) distribution, which extends the two-parameter Rama distribution and has the Rama distribution as a special case. The GWR distribution has the ability to model data sets that have positive skewness and upside-down bathtub shape hazard rate. Expressions for mathematical and reliability properties of the GWR distribution have been derived. Estimation of parameters was achieved using the method of maximum likelihood estimation and a simulation was performed to verify the stability of the maximum likelihood estimates of the model parameters. The asymptotic confidence intervals of the parameters of the proposed distribution are obtained. The applicability of the GWR distribution was illustrated with a real data set and the results obtained show that the GWR distribution is a better candidate for the data than the other competing distributions being investigated.

Sign in / Sign up

Export Citation Format

Share Document