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.

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 The Complementary Exponentiated Lomax-Poisson Distribution with Applications to Bladder Cancer and Failure Data

2021 ◽  
Vol 50 (3) ◽  
pp. 77-105
Author(s):  
Devendra Kumar ◽  
Mazen Nassar ◽  
Ahmed Z. Afify ◽  
Sanku Dey
Keyword(s):  
Least Squares ◽  
Poisson Distribution ◽  
Weighted Least Squares ◽  
Real Data ◽  
Random Variable ◽  
Model Parameters ◽  
Data Sets ◽  
Monte Carlo Simulation Study ◽  
Failure Data ◽  
New Distribution

A new continuous four-parameter lifetime distribution is introduced by compounding the distribution of the maximum of a sequence of an independently identically exponentiated Lomax distributed random variables and zero truncated Poisson random variable, defined as the complementary exponentiated Lomax Poisson (CELP) distribution. The new distribution which exhibits decreasing and upside down bathtub shaped density while the distribution has the ability to model lifetime data with decreasing, increasing and upside-down bathtub shaped failure rates. The new distribution has a number of well-known lifetime special sub-models, such as Lomax-zero truncated Poisson distribution, exponentiated Pareto-zero truncated Poisson distribution and Pareto- zero truncated Poisson distribution. A comprehensive account of the mathematical and statistical properties of the new distribution is presented. The model parameters are obtained by the methods of maximum likelihood, least squares, weighted least squares, percentiles, maximum product of spacing and Cram\'er-von-Mises and compared them using Monte Carlo simulation study. We illustrate the performance of the proposed distribution by means of two real data sets and both the data sets show the new distribution is more appropriate as compared to the transmuted Lomax, beta exponentiated Lomax, McDonald Lomax, Kumaraswamy Lomax, Weibull Lomax, Burr X Lomax and Lomax distributions.

scholarly journals Theory and Applications of the Unit Gamma/Gompertz Distribution

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1850
Author(s):  
Rashad A. R. Bantan ◽  
Farrukh Jamal ◽  
Christophe Chesneau ◽  
Mohammed Elgarhy
Keyword(s):  
Stochastic Ordering ◽  
Real Data ◽  
Rate Function ◽  
The Other ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
Gompertz Distribution ◽  
Probability And Statistics ◽  
Analytical Behavior

Unit distributions are commonly used in probability and statistics to describe useful quantities with values between 0 and 1, such as proportions, probabilities, and percentages. Some unit distributions are defined in a natural analytical manner, and the others are derived through the transformation of an existing distribution defined in a greater domain. In this article, we introduce the unit gamma/Gompertz distribution, founded on the inverse-exponential scheme and the gamma/Gompertz distribution. The gamma/Gompertz distribution is known to be a very flexible three-parameter lifetime distribution, and we aim to transpose this flexibility to the unit interval. First, we check this aspect with the analytical behavior of the primary functions. It is shown that the probability density function can be increasing, decreasing, “increasing-decreasing” and “decreasing-increasing”, with pliant asymmetric properties. On the other hand, the hazard rate function has monotonically increasing, decreasing, or constant shapes. We complete the theoretical part with some propositions on stochastic ordering, moments, quantiles, and the reliability coefficient. Practically, to estimate the model parameters from unit data, the maximum likelihood method is used. We present some simulation results to evaluate this method. Two applications using real data sets, one on trade shares and the other on flood levels, demonstrate the importance of the new model when compared to other unit models.

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 The Alpha Power Transformation Family: Properties and Applications

2019 ◽  
pp. 525-545 ◽  
Author(s):  
Mohamed E. Mead ◽  
Gauss M. Cordeiro ◽  
Ahmed Z. Afify ◽  
Hazem Al Mofleh
Keyword(s):  
Real Data ◽  
Likelihood Method ◽  
Model Parameters ◽  
Power Transformation ◽  
Data Sets ◽  
Alpha Power ◽  
Weibull Distributions ◽  
Exponentiated Weibull ◽  
Rate Functions ◽  
Modified Weibull

Mahdavi A. and Kundu D. (2017) introduced a family for generating univariate distributions called the alpha power transformation. They studied as a special case the properties of the alpha power transformed exponential distribution. We provide some mathematical properties of this distribution and define a four-parameter lifetime model called the alpha power exponentiated Weibull distribution. It generalizes some well-known lifetime models such as the exponentiated exponential, exponentiated Rayleigh, exponentiated Weibull and Weibull distributions. The importance of the new distribution comes from its ability to model monotone and non-monotone failure rate functions, which are quite common in reliability studies. We derive some basic properties of the proposed distribution including quantile and generating functions, moments and order statistics. The maximum likelihood method is used to estimate the model parameters. Simulation results investigate the performance of the estimates. We illustrate the importance of the proposed distribution over the McDonald Weibull, beta Weibull, modified Weibull, transmuted Weibull and exponentiated Weibull distributions by means of two real data sets.

scholarly journals Hot News Recommendation System from Heterogeneous Websites Based on Bayesian Model

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Zhengyou Xia ◽  
Shengwu Xu ◽  
Ningzhong Liu ◽  
Zhengkang Zhao
Keyword(s):  
Bayesian Model ◽  
Recommendation System ◽  
Research Work ◽  
Joint Probability ◽  
Real Data ◽  
Online News ◽  
City Government ◽  
Data Sets ◽  
News Websites ◽  
News Recommendation

The most current news recommendations are suitable for news which comes from a single news website, not for news from different heterogeneous news websites. Previous researches about news recommender systems based on different strategies have been proposed to provide news personalization services for online news readers. However, little research work has been reported on utilizing hundreds of heterogeneous news websites to provide top hot news services for group customers (e.g., government staffs). In this paper, we propose a hot news recommendation model based on Bayesian model, which is from hundreds of different news websites. In the model, we determine whether the news is hot news by calculating the joint probability of the news. We evaluate and compare our proposed recommendation model with the results of human experts on the real data sets. Experimental results demonstrate the reliability and effectiveness of our method. We also implement this model in hot news recommendation system of Hangzhou city government in year 2013, which achieves very good results.

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 A New Burr XII-Weibull-Logarithmic Distribution for Survival and Lifetime Data Analysis: Model, Theory and Applications

Stats ◽  
2018 ◽  
Vol 1 (1) ◽  
pp. 77-91
Author(s):  
Broderick Oluyede ◽  
Boikanyo Makubate ◽  
Adeniyi Fagbamigbe ◽  
Precious Mdlongwa
Keyword(s):  
Likelihood Estimation ◽  
Real Data ◽  
Model Parameters ◽  
Data Sets ◽  
Analysis Model ◽  
Conditional Moments ◽  
Compound Distribution ◽  
Lifetime Data Analysis ◽  
Logarithmic Distribution ◽  
New Distribution

A new compound distribution called Burr XII-Weibull-Logarithmic (BWL) distribution is introduced and its properties are explored. This new distribution contains several new and well known sub-models, including Burr XII-Exponential-Logarithmic, Burr XII-Rayleigh-Logarithmic, Burr XII-Logarithmic, Lomax-Exponential-Logarithmic, Lomax–Rayleigh-Logarithmic, Weibull, Rayleigh, Lomax, Lomax-Logarithmic, Weibull-Logarithmic, Rayleigh-Logarithmic, and Exponential-Logarithmic distributions. Some statistical properties of the proposed distribution including moments and conditional moments are presented. Maximum likelihood estimation technique is used to estimate the model parameters. Finally, applications of the model to real data sets are presented to illustrate the usefulness of the proposed distribution.

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.

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