scholarly journals Comparing Different Estimators for the shape Parameter and the Reliability function of Kumaraswamy Distribution

2019 ◽  
Vol 25 (116) ◽  
pp. 199-225
Author(s):  
Jinan Abbas Naser Al-Obedy
Keyword(s):  
Shape Parameter ◽  
Reliability Function ◽  
Bayes Estimation ◽  
Likelihood Method ◽  
Prior Distributions ◽  
Squared Error Loss Function ◽  
Kumaraswamy Distribution ◽  
Chi Squared ◽  
Two Parameters ◽  
Mean Square Errors

In this paper, we used maximum likelihood method and the Bayesian method to estimate the shape parameter (θ), and reliability function (R(t)) of the Kumaraswamy distribution with two parameters l , θ (under assuming the exponential distribution, Chi-squared distribution and Erlang-2 type distribution as prior distributions), in addition to that we used method of moments for estimating the parameters of the prior distributions. Bayes estimators derived under the squared error loss function. We conduct simulation study, to compare the performance for each estimator, several values of the shape parameter (θ) from Kumaraswamy distribution for data-generating, for different samples sizes (small, medium, and large). Simulation results have shown that the Best method is the Bayes estimation according to the smallest values of mean square errors(MSE) for all samples sizes (n).  

scholarly journals A Comparative Study on the Double Prior for Reliability Kumaraswamy Distribution with Numerical Solution

2020 ◽  
Vol 17 (1) ◽  
pp. 0159
Author(s):  
Abraheem Et al.
Keyword(s):  
Numerical Solution ◽  
Shape Parameter ◽  
Expansion Method ◽  
Reliability Function ◽  
Distribution Functions ◽  
Kumaraswamy Distribution ◽  
Bayes Methods ◽  
Probability Distribution Functions ◽  
Symmetric Loss ◽  
Log Normal

This work, deals with Kumaraswamy distribution. Kumaraswamy (1976, 1978) showed well known probability distribution functions such as the normal, beta and log-normal but in (1980) Kumaraswamy developed a more general probability density function for double bounded random processes, which is known as Kumaraswamy’s distribution. Classical maximum likelihood and Bayes methods estimator are used to estimate the unknown shape parameter (b). Reliability function are obtained using symmetric loss functions by using three types of informative priors two single priors and one double prior. In addition, a comparison is made for the performance of these estimators with respect to the numerical solution which are found using expansion method. The results showed that the reliability estimator under Rn and R3 is the best.

scholarly journals Bayes Estimation of the Reliability Function of Pareto Distribution Under Three Different Loss Functions

2020 ◽  
Author(s):  
Gaurav Shukla ◽  
Umesh Chandra ◽  
Vinod Kumar
Keyword(s):  
Shape Parameter ◽  
Pareto Distribution ◽  
Risk Function ◽  
Simulated Data ◽  
Reliability Function ◽  
Minimum Variance ◽  
Bayes Estimation ◽  
Loss Functions ◽  
Bayes Estimators ◽  
Data Set

In this paper, we have proposed Bayes estimators of shape parameter of Pareto distribution as well as reliability function under SELF, QLF and APLF loss functions. For better understanding of Bayesian approach, we consider Jeffrey’s prior as non-informative prior, exponential and gamma priors as informative priors. The proposed estimators have been compared with Maximum likelihood estimator (MLE) and the uniformly minimum variance unbiased estimator (UMVUE). Moreover, the current study also derives the expressions for risk function under these three loss functions. The results obtained have been illustrated with the real as well as simulated data set.

scholarly journals Bayesian and Non - Bayesian Inference for Shape Parameter and Reliability Function of Basic Gompertz Distribution

2020 ◽  
Vol 17 (3) ◽  
pp. 0854
Author(s):  
Manahel Awad ◽  
Huda Rashed
Keyword(s):  
Shape Parameter ◽  
Simulation Method ◽  
Reliability Function ◽  
Monte Carlo Simulation Method ◽  
Scale Invariant ◽  
Squared Error Loss Function ◽  
Gompertz Distribution ◽  
Mean Squared Errors ◽  
Squared Error ◽  
Informative Prior

In this paper, some estimators of the unknown shape parameter and reliability function  of Basic Gompertz distribution (BGD) have been obtained, such as MLE, UMVUE, and MINMSE, in addition to estimating Bayesian estimators under Scale invariant squared error loss function assuming informative prior represented by Gamma distribution and non-informative prior by using Jefferys prior. Using Monte Carlo simulation method, these estimators of the shape parameter and R(t), have been compared based on mean squared errors and integrated mean squared, respectively

scholarly journals Estimating the Reliability Function of some Stress- Strength Models for the Generalized Inverted Kumaraswamy Distribution

2021 ◽  
pp. 240-251
Author(s):  
Hakeem Hussain Hamad ◽  
Nada Sabah Karam
Keyword(s):  
Maximum Likelihood ◽  
Shape Parameter ◽  
Maximum Likelihood Estimators ◽  
Reliability Function ◽  
Least Square ◽  
Mean Square ◽  
Kumaraswamy Distribution ◽  
Scale Parameters ◽  
Strength Models ◽  
Best Estimator

This paper discusses reliability of the stress-strength model. The reliability functions 𝑅1 and 𝑅2 were obtained for a component which has an independent strength and is exposed to two and three stresses, respectively. We used the generalized inverted Kumaraswamy distribution GIKD with unknown shape parameter as well as known shape and scale parameters. The parameters were estimated from the stress- strength models, while the reliabilities 𝑅1, 𝑅2 were estimated by three methods, namely the Maximum Likelihood,  Least Square, and Regression.  A numerical simulation study a comparison between the three estimators by mean square error is performed. It is found that best estimator between the three estimators is Maximum likelihood estimators.  

scholarly journals A Comparison of the Methods for Estimation of Reliability Function for Burr-XII Distribution by Using Simulation.

2013 ◽  
Vol 10 (1) ◽  
pp. 85-96
Author(s):  
Baghdad Science Journal
Keyword(s):  
Empirical Study ◽  
Sample Size ◽  
Mean Square Error ◽  
Shape Parameter ◽  
Reliability Function ◽  
Mean Square ◽  
Simulation Experiments ◽  
Two Parameters ◽  
Parameter Values ◽  
Better Than

This deals with estimation of Reliability function and one shape parameter (?) of two- parameters Burr – XII , when ?(shape parameter is known) (?=0.5,1,1.5) and also the initial values of (?=1), while different sample shze n= 10, 20, 30, 50) bare used. The results depend on empirical study through simulation experiments are applied to compare the four methods of estimation, as well as computing the reliability function . The results of Mean square error indicates that Jacknif estimator is better than other three estimators , for all sample size and parameter values

scholarly journals مقارنة مقدرات بيز لدالة المعولية لتوزيع باريتو من النوع الاول باستعمال دوال معلوماتية مضاعفة مختلفة

2019 ◽  
Vol 25 (113) ◽  
Author(s):  
جنان عباس ناصر
Keyword(s):  
Prior Distribution ◽  
Reliability Function ◽  
Bayes Estimation ◽  
Erlang Distribution ◽  
Type I ◽  
Informative Priors ◽  
Squared Error Loss Function ◽  
True Value ◽  
Squared Error ◽  
Simulation Results

The comparison of double informative priors which are assumed for the reliability function of Pareto type I distribution. To estimate the reliability function of Pareto type I distribution by using Bayes estimation, will be  used two different kind of information in the Bayes estimation; two different priors have been selected for the parameter of Pareto  type I distribution . Assuming distribution of three double prior’s chi- gamma squared distribution, gamma - erlang distribution, and erlang- exponential distribution as double priors. The results of the derivaties of these estimators under the squared error loss function with two different double priors. Using the simulation technique, to compare the performance for each estimator, several cases from pareto type I distribution for data generating, and for different samples sizes (small, medium, and large). It has been obtained from the simulation results the double prior distribution  of gamma-erlang distribution with give a good estimation for reliability function when the true value for for all .Also the double prior distribution chi- gamma square distribution with give good estimation for reliability function when the true value for all t. And the same thing for with the values of the parameters and for all t except t=1.3. It has obtained a good estimation for reliability function (), when the double prior distribution is chi-gamma square distribution with at the true value for for all t.

scholarly journals Bayes Estimators for the Parameter of the Inverted Exponential Distribution Under different Double informative priors

2018 ◽  
Vol 24 (103) ◽  
pp. 18
Author(s):  
جنان عباس ناصر
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Exponential Distribution ◽  
Likelihood Estimation ◽  
Bayes Estimation ◽  
Erlang Distribution ◽  
Mean Square ◽  
Informative Priors ◽  
Chi Squared ◽  
Mean Square Errors

In this paper, we present a comparison of double informative priors which are assumed for the parameter of inverted exponential distribution.To estimate the parameter of inverted exponential distribution by using Bayes estimation ,will be  used two different kind of information in the Bayes estimation; two different priors have been selected for the parameter of inverted exponential distribution. Also assumed Chi-squared - Gamma distribution, Chi-squared - Erlang distribution, and- Gamma- Erlang distribution as double priors. The results are the derivations of these estimators under the squared error loss function with three different double priors. Additionally Maximum likelihood estimation method (MLE) was used  to estimate the parameter of inverted exponential distribution .We used simulation technique, to compare the performance for each estimator, several cases from inverted exponential distribution for data generating, for different samples sizes (small, medium, and large).Simulation results shown that the best method is the bayes  estimation according to the smallest values of mean square errors( MSE) for all samples sizes (n) comparative to the estimated values by using MLE . According to obtained results, we see that when the double prior distribution for  is Gamma- Erlang distribution for some values for the parameters a, b & given the best results according to the smallest values of mean square errors (MSE) comparative to the same values which obtained by using Maximum likelihood estimation (MLE) for the assuming true values for and for all samples sizes.  

scholarly journals A Two Parameters Rani Distribution: Estimation and Tests for Right Censoring Data with an Application

2021 ◽  
pp. 1037-1049
Author(s):  
Amer Ibrahim Al-Omari ◽  
Khaoula Aidi ◽  
Nacira Seddik-Ameur
Keyword(s):  
Hazard Function ◽  
Goodness Of Fit ◽  
Reliability Function ◽  
Parameters Estimation ◽  
Right Censoring ◽  
Likelihood Method ◽  
Model Parameters ◽  
Right Censored Data ◽  
Two Parameters ◽  
Reversed Hazard Function

In this paper, we developed a new distribution, namely the two parameters Rani distribution (TPRD). Some statistical properties of the proposed distribution are derived including the moments, moment-generating function, reliability function, hazard function, reversed hazard function, odds function, the density function of order statistics, stochastically ordering, and the entropies. The maximum likelihood method is used for model parameters estimation. Following the same approach suggested by Bagdonavicius and Nikulin (2011), modified chi squared goodness-of-fit tests are constructed for right censored data and some tests for right data is considered. An application study is presented to illustrate the ability of the suggested model in fitting aluminum reduction cells sets and the strength data of glass of the aircraft window.

Bayes Estimation of Augmenting Gamma Strength Reliability of a System under Non-informative Prior Distributions

2017 ◽  
Vol 69 (1) ◽  
pp. 87-102 ◽  
Author(s):  
N. Chandra ◽  
V.K. Rathaur
Keyword(s):  
Loss Function ◽  
Bayes Estimation ◽  
Linex Loss Function ◽  
Squared Error Loss Function ◽  
Squared Error ◽  
Linex Loss ◽  
Augmentation Strategy ◽  
Mean Square Errors ◽  
Informative Prior Distributions ◽  
Common Shape

In this article, Bayes estimation of system’s augmented strength reliability is studied under squared-error loss function (SELF) and LINEX loss function (LLF) for the generalized case of augmentation strategy plan (ASP). ASP is helpful in enhancing the strength reliability of weaker system/equipment. It is assumed that the stress (usual) and augmented strength follow a gamma distribution with common shape [Formula: see text] and scale [Formula: see text] parameters. A simulation study is performed for the comparisons of Bayes estimators of augmented strength reliability for non-informative types of prior (uniform and Jeffrey’s priors) with maximum likelihood estimators on the basis of their mean square errors and the absolute biases by simulating 1,000 Monte Carlo samples. The proposed methods are compared by analysing real and simulated datasets for illustration purpose.

scholarly journals Non Bayesian estimation for survival and hazard function of weighted Rayleigh distribution (b)

2020 ◽  
pp. 3059-3071
Author(s):  
Saad Adnan Zain
Keyword(s):  
Hazard Function ◽  
Shape Parameter ◽  
Survival Function ◽  
Real Data ◽  
Rayleigh Distribution ◽  
Likelihood Method ◽  
Data Sets ◽  
New Class ◽  
The Moment ◽  
Two Parameters

In this paper, we proposed a new class of Weighted Rayleigh Distribution based on two parameters, one is scale parameter and the other is shape parameter which introduced in Rayleigh distribution. The main properties of this class are derived and investigated in . The moment method and maximum likelihood method are used to obtain estimators of parameters, survival function and hazard function. Real data sets are collected to investigate two methods which depend it in this study. A comparison was made between two methods of estimation.

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