scholarly journals Estimating Stress-Strength Model for Weighted Lomax Distribution

2021 ◽  
pp. 19-31
Author(s):  
M. M. E. Abd El-Monsef ◽  
Ghareeb A. Marei ◽  
N. M. Kilany
Keyword(s):  
Waiting Times ◽  
Real Data ◽  
Reliability Function ◽  
Data Sets ◽  
Strength Model ◽  
Reliability Parameter ◽  
Strength Parameters ◽  
Monte Carlo Simulation Study ◽  
Satisfactory Performance ◽  
Bayesian Estimators

This paper aims to estimate the stress-strength reliability parameter  when  and  are follow the weighted Lomax (WL) distribution. The behavior of stress-strength parameters and reliability have been studied by using maximum likelihood and Bayesian estimators through the Monte Carlo simulation study which carried out showing satisfactory performance of the estimators obtained. Finally, two real data sets representing waiting times before service of the customers of two banks A and B are fitted using the WL distribution and used to estimate the stress-strength parameters and reliability function.

scholarly journals On Reliability in a Multicomponent Stress-Strength Model with Power Lindley Distribution

2018 ◽  
Vol 41 (2) ◽  
pp. 251-267 ◽  
Author(s):  
Abbas Pak ◽  
Arjun Kumar Gupta ◽  
Nayereh Bagheri Khoolenjani
Keyword(s):  
Interval Estimation ◽  
Parametric Bootstrap ◽  
Real Data ◽  
Credible Interval ◽  
Data Sets ◽  
Strength Model ◽  
Reliability Parameter ◽  
Posterior Density ◽  
Bayes Estimate ◽  
Highest Posterior Density

In this paper  we study the reliability of a multicomponent stress-strength model assuming that the components follow power Lindley model.  The maximum likelihood estimate of the reliability parameter and its asymptotic confidence interval are obtained. Applying the parametric Bootstrap technique, interval estimation of the reliability is presented.  Also, the Bayes estimate and highest posterior density credible interval of the reliability parameter are derived using suitable priors on the parameters. Because there is no closed form for the Bayes estimate, we use the Markov Chain Monte Carlo method to obtain approximate Bayes  estimate of the reliability. To evaluate the performances of different procedures,  simulation studies are conducted and an example of real data sets is provided.

scholarly journals Type II General Exponential Class of Distributions

2019 ◽  
pp. 503-523 ◽  
Author(s):  
G. G. Hamedani ◽  
Mahdi Rasekhi ◽  
Sayed Najibi ◽  
Haitham M. Yousof ◽  
Morad Alizadeh
Keyword(s):  
Hazard Function ◽  
Residual Life ◽  
Real Data ◽  
Random Variable ◽  
Reliability Function ◽  
Interval Length ◽  
Data Sets ◽  
Type Ii ◽  
Mean Squared Errors ◽  
New Class

In this paper, a new class of continuous distributions with two extra positive parameters is introduced and is called the Type II General Exponential (TIIGE) distribution. Some special models are presented. Asymptotics, explicit expressions for the ordinary and incomplete moments, moment residual life, reversed residual life, quantile and generating functions and stress-strengh reliability function are derived. Characterizations of this family are obtained based on truncated moments, hazard function, conditional expectation of certain functions of the random variable are obtained. The performance of the maximum likelihood estimators in terms of biases, mean squared errors and confidence interval length is examined by means of a simulation study. Two real data sets are used to illustrate the application of the proposed class.

scholarly journals A New Extended-X Family of Distributions: Properties and Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Mi Zichuan ◽  
Saddam Hussain ◽  
Anum Iftikhar ◽  
Muhammad Ilyas ◽  
Zubair Ahmad ◽  
...  
Keyword(s):  
Real Data ◽  
Model Parameters ◽  
Data Sets ◽  
Statistical Distributions ◽  
Reliability Engineering ◽  
Monte Carlo Simulation Study ◽  
Diverse Range ◽  
Heavy Tailed ◽  
Log Normal ◽  
Extended Weibull Distribution

During the past couple of years, statistical distributions have been widely used in applied areas such as reliability engineering, medical, and financial sciences. In this context, we come across a diverse range of statistical distributions for modeling heavy tailed data sets. Well-known distributions are log-normal, log-t, various versions of Pareto, log-logistic, Weibull, gamma, exponential, Rayleigh and its variants, and generalized beta of the second kind distributions, among others. In this paper, we try to supplement the distribution theory literature by incorporating a new model, called a new extended Weibull distribution. The proposed distribution is very flexible and exhibits desirable properties. Maximum likelihood estimators of the model parameters are obtained, and a Monte Carlo simulation study is conducted to assess the behavior of these estimators. Finally, we provide a comparative study of the newly proposed and some other existing methods via analyzing three real data sets from different disciplines such as reliability engineering, medical, and financial sciences. It has been observed that the proposed method outclasses well-known distributions on the basis of model selection criteria.

scholarly journals The Transmuted Odd Lindley-G Family of Distributions

2018 ◽  
pp. 1-25 ◽  
Author(s):  
Hesham Reyad ◽  
Farrukh Jamal ◽  
Soha Othman ◽  
G. G. Hamedani
Keyword(s):  
Information Matrix ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Data Sets ◽  
Strength Model ◽  
New Family ◽  
Mathematical Properties ◽  
Probability Weighted Moments ◽  
Family Of Distributions

We propose a new generator of univariate continuous distributions with two extra parameters called the transmuted odd-Lindley generator which extends the odd Lindely-G family introduced by Gomes-Silva et al. [1]. Some mathematical properties of the new generator such as, the ordinary and incomplete moments, generating function, stress strength model, Rényi entropy, probability weighted moments and order statistics are investigated. Certain characterisations of the proposed family are estimated. We discuss the maximum likelihood estimates and the observed information matrix for the model parameters. The potentiality of the new family is illustrated by means of five applications to real data sets.  

scholarly journals Transmuted Singh-Maddala Distribution: A new Flexible and Upside-Down Bathtub Shaped Hazard Function Distribution

2017 ◽  
Vol 40 (1) ◽  
pp. 1-27 ◽  
Author(s):  
Mirza Naveed Shahzad ◽  
Faton Merovci ◽  
Zahid Asghar
Keyword(s):  
Hazard Function ◽  
Likelihood Estimation ◽  
Real Data ◽  
Reliability Function ◽  
Data Sets ◽  
Distribution Models ◽  
Unknown Parameters ◽  
Bathtub Shape ◽  
Parent Distribution ◽  
Special Cases

The Singh-Maddala distribution is very popular to analyze the data on income, expenditure, actuarial, environmental, and reliability related studies. To enhance its scope and application, we propose four parameters transmutedSingh-Maddala distribution, in this study. The proposed distribution is relatively more flexible than the parent distribution to model a variety of data sets. Its basic statistical properties, reliability function, and behaviors of the hazard function are derived. The hazard function showed the decreasing and an upside-down bathtub shape that is required in various survival analysis. The order statistics and generalized TL-moments with their special cases such as L-, TL-, LL-, and LH-moments are also explored. Furthermore, the maximum likelihood estimation is used to estimate the unknown parameters of the transmuted Singh-Maddala distribution. The real data sets are considered to illustrate the utility and potential of the proposed model. The results indicate that the transmuted Singh-Maddala distribution models the datasets better than its parent distribution.

scholarly journals Marshall-Olkin Alpha Power Rayleigh Distribution: Properties, Characterizations, Estimation and Engineering applications

2021 ◽  
pp. 745-760
Author(s):  
Ehab Mohamed Almetwally ◽  
Ahmed Z. Afify ◽  
G. G. Hamedani
Keyword(s):  
Maximum Likelihood ◽  
Hazard Function ◽  
Real Data ◽  
Rayleigh Distribution ◽  
Estimation Methods ◽  
Data Sets ◽  
Alpha Power ◽  
Monte Carlo Simulation Study ◽  
Bootstrap Estimation ◽  
Proposed Model

In this paper, we introduce a new there-parameter Rayleigh distribution, called the Marshall-Olkin alpha power Rayleigh (MOAPR) distribution. Some statistical properties of the MOAPR distribution are obtained. The proposed model is characterized based on truncated moments and reverse hazard function. The maximum likelihood and bootstrap estimation methods are considered to estimate the MOPAR parameters. A Monte Carlo simulation study is performed to compare the maximum likelihood and bootstrap estimation methods. Superiority of the MOAPR distribution over some well-known distributions is illustrated by means of two real data sets.

scholarly journals A family of Gamma-generated distributions: Statistical properties and applications

2021 ◽  
pp. 096228022110092
Author(s):  
Hormatollah Pourreza ◽  
Ezzatallah Baloui Jamkhaneh ◽  
Einolah Deiri
Keyword(s):  
Weibull Distribution ◽  
Real Data ◽  
Statistical Properties ◽  
Cumulative Distribution ◽  
Data Sets ◽  
Monte Carlo Simulation Study ◽  
Hazard Functions ◽  
Distribution Probability ◽  
Method Of Maximum Likelihood ◽  
Special Case

In this paper, we concentrate on the statistical properties of Gamma-X family of distributions. A special case of this family is the Gamma-Weibull distribution. Therefore, the statistical properties of Gamma-Weibull distribution as a sub-model of Gamma-X family are discussed such as moments, variance, skewness, kurtosis and Rényi entropy. Also, the parameters of the Gamma-Weibull distribution are estimated by the method of maximum likelihood. Some sub-models of the Gamma-X are investigated, including the cumulative distribution, probability density, survival and hazard functions. The Monte Carlo simulation study is conducted to assess the performances of these estimators. Finally, the adequacy of Gamma-Weibull distribution in data modeling is verified by the two clinical real data sets. Mathematics Subject Classification: 62E99; 62E15

Regression trees with splitting based on changes of dependencies among covariates

2021 ◽  
Vol 25 (3) ◽  
pp. 687-710
Author(s):  
Mostafa Boskabadi ◽  
Mahdi Doostparast
Keyword(s):  
Regression Trees ◽  
Real Data ◽  
Data Sets ◽  
Monte Carlo Simulation Study ◽  
New Approach ◽  
Homogeneous Groups ◽  
Mathematical Properties ◽  
Proposed Model ◽  
Regression Problems ◽  
Dependency Structures

Regression trees are powerful tools in data mining for analyzing data sets. Observations are usually divided into homogeneous groups, and then statistical models for responses are derived in the terminal nodes. This paper proposes a new approach for regression trees that considers the dependency structures among covariates for splitting the observations. The mathematical properties of the proposed method are discussed in detail. To assess the accuracy of the proposed model, various criteria are defined. The performance of the new approach is assessed by conducting a Monte-Carlo simulation study. Two real data sets on classification and regression problems are analyzed by using the obtained results.

scholarly journals Bayesian inference on reliability in a multicomponent stress-strength bathtub-shaped model based on record values

2019 ◽  
pp. 431-444 ◽  
Author(s):  
Abbas Pak ◽  
Nayereh Bagheri Khoolenjani ◽  
Manoj Kumar Rastogi
Keyword(s):  
Real Data ◽  
Record Values ◽  
Loss Functions ◽  
Data Sets ◽  
Simulation Studies ◽  
Reliability Parameter ◽  
Bayes Estimates ◽  
Squared Error ◽  
Current Value ◽  
Strength Models

In the literature, there are a well-developed estimation techniques for the reliability assessment in multicomponent stress-strength models when the information about all the experimental units are available. However, in real applications, only observations that exceed (or fall below) the current value may be recorded. In this paper, assuming that the components of the system follow bathtub-shaped distribution, we investigate Bayesian estimation of the reliability of a multicomponent stress-strength system when the available data are reported in terms of record values. Considering squared error, linex and entropy loss functions, various Bayes estimates of the reliability are derived. Because there are not closed forms for the Bayes estimates, we will use Lindley’s method to calculate the approximate Bayes estimates. Further, for comparison purposes, the maximum likelihood estimate of the reliability parameter is obtained. Finally, simulation studies are conducted in order to evaluate the performances of the proposed procedures and analysis of real data sets is provided.

scholarly journals THE POWER MUTH DISTRIBUTION∗

2017 ◽  
Vol 22 (2) ◽  
pp. 186-201 ◽  
Author(s):  
Pedro Jodra ◽  
Hector Wladimir Gomez ◽  
Maria Dolores Jimenez-Gamero ◽  
Maria Virtudes Alba-Fernandez
Keyword(s):  
Probability Distributions ◽  
Real Data ◽  
Rate Function ◽  
Data Sets ◽  
Estimation Of Parameters ◽  
Failure Rate Function ◽  
Monte Carlo Simulation Study ◽  
New Model ◽  
Practical Usefulness ◽  
Method Of Maximum Likelihood

Muth introduced a probability distribution with application in reliability theory. We propose a new model from the Muth law. This paper studies its statistical properties, such as the computation of the moments, computer generation of pseudo-random data and the behavior of the failure rate function, among others. The estimation of parameters is carried out by the method of maximum likelihood and a Monte Carlo simulation study assesses the performance of this method. The practical usefulness of the new model is illustrated by means of two real data sets, showing that it may provide a better fit than other probability distributions.

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