Bayesian Approximation Techniques for the Generalized Inverted Exponential Distribution

The Bayesian estimation of the scale parameter of a Laplace Distribution is obtained using two approximation techniques, like Normal approximation and Tierney and Kadane (T-K) approximation, under different informative priors.

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The Approximation of Sum of Independent Distributions by the Erlang Distribution Function

Nonlinear Analysis Modelling and Control ◽

10.15388/na.2002.7.1.15202 ◽

2002 ◽

Vol 7 (1) ◽

pp. 55-60 ◽

Cited By ~ 1

Author(s):

Antanas Karoblis

Keyword(s):

Distribution Function ◽

Exponential Distribution ◽

Queueing Theory ◽

Erlang Distribution ◽

Estimation Of Error

The exponential distribution and the Erlang distribution function are been used in numerous areas of mathematics, and specifically in the queueing theory. Such and similar applications emphasize the importance of estimation of error of approximation by the Erlang distribution function. The article gives an analysis and technique of error’s estimation of an accuracy of such approximation, especially in some specific cases.

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Optimal Nonlinear Feedback Control by Using Galerkin Approximation Techniques

AIAA Guidance, Navigation, and Control Conference ◽

10.2514/6.2009-5990 ◽

2009 ◽

Author(s):

Rajnish Sharma ◽

Srinivas Vadali

Keyword(s):

Feedback Control ◽

Galerkin Approximation ◽

Nonlinear Feedback Control ◽

Nonlinear Feedback ◽

Approximation Techniques

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The Comparison Between the Bayes Estimator and the Maximum Likelihood Estimator of the Reliability Function for Negative Exponential Distribution

Ibn AL- Haitham Journal For Pure and Applied Science ◽

10.30526/2017.ihsciconf.1815 ◽

2018 ◽

pp. 439

Author(s):

Hazim Mansour Gorgees ◽

Bushra Abdualrasool Ali ◽

Raghad Ibrahim Kathum

Keyword(s):

Maximum Likelihood ◽

Maximum Likelihood Estimator ◽

Exponential Distribution ◽

Reliability Function ◽

Bayes Estimator ◽

Likelihood Estimator ◽

Monte Carlo Simulation Technique ◽

Negative Exponential Distribution ◽

Negative Exponential ◽

Better Than

In this paper, the maximum likelihood estimator and the Bayes estimator of the reliability function for negative exponential distribution has been derived, then a Monte –Carlo simulation technique was employed to compare the performance of such estimators. The integral mean square error (IMSE) was used as a criterion for this comparison. The simulation results displayed that the Bayes estimator performed better than the maximum likelihood estimator for different samples sizes.

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Evaluation for estimating of the PDF and the CDF of Generalized Inverted Exponential Distribution with Application in Industry

Advances in Mathematics: Scientific Journal ◽

10.37418/amsj.9.1.39 ◽

2020 ◽

pp. 507-522

Author(s):

Parisa Torkaman

Keyword(s):

Least Squares ◽

Exponential Distribution ◽

Mean Squared Error ◽

Weighted Least Squares ◽

Real Data ◽

Minimum Variance ◽

Cumulative Distribution ◽

Estimation Methods ◽

Data Set ◽

Better Than

The generalized inverted exponential distribution is introduced as a lifetime model with good statistical properties. This paper, the estimation of the probability density function and the cumulative distribution function of with five different estimation methods: uniformly minimum variance unbiased(UMVU), maximum likelihood(ML), least squares(LS), weighted least squares (WLS) and percentile(PC) estimators are considered. The performance of these estimation procedures, based on the mean squared error (MSE) by numerical simulations are compared. Simulation studies express that the UMVU estimator performs better than others and when the sample size is large enough the ML and UMVU estimators are almost equivalent and efficient than LS, WLS and PC. Finally, the result using a real data set are analyzed.

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A simulation comparison of quantile approximation techniques for compound distributions popular in operational risk

The Journal of Operational Risk ◽

10.21314/jop.2016.171 ◽

2016 ◽

Vol 11 (1) ◽

pp. 23-48 ◽

Cited By ~ 3

Author(s):

P. J. de Jongh ◽

Tertius de Wet ◽

Kevin Panman ◽

Helgard Raubenheimer

Keyword(s):

Operational Risk ◽

Compound Distributions ◽

Approximation Techniques ◽

Quantile Approximation

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Ehrenfest urn models

Journal of Applied Probability ◽

10.1017/s0021900200108708 ◽

1965 ◽

Vol 2 (02) ◽

pp. 352-376 ◽

Cited By ~ 25

Author(s):

Samuel Karlin ◽

James McGregor

Keyword(s):

Exponential Distribution ◽

Continuous Time ◽

Random Variables ◽

Independent Random Variables ◽

Urn Models ◽

Time Intervals ◽

Negative Exponential Distribution ◽

Negative Exponential ◽

Random Times

In the Ehrenfest model with continuous time one considers two urns and N balls distributed in the urns. The system is said to be in stateiif there areiballs in urn I, N −iballs in urn II. Events occur at random times and the time intervals T between successive events are independent random variables all with the same negative exponential distributionWhen an event occurs a ball is chosen at random (each of theNballs has probability 1/Nto be chosen), removed from its urn, and then placed in urn I with probabilityp, in urn II with probabilityq= 1 −p, (0 <p< 1).

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