Comparison of the Bayesian Estimations Under Different Loss Function and Maximum Likelihood Estimation for Rayleigh Distribution

We introduce the transmuted modified Inverse Rayleighdistribution by using quadratic rank transmutation map (QRTM), whichextends the modified Inverse Rayleigh distribution. A comprehensiveaccount of the mathematical properties of the transmuted modified InverseRayleigh distribution are discussed. We derive the quantile, moments,moment generating function, entropy, mean deviation, Bonferroni andLorenz curves, order statistics and maximum likelihood estimation Theusefulness of the new model is illustrated using real lifetime data.

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Modelling Significant Wave Height Data of North Sea: Rayleigh vs Weibull Distribution

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.157-158.652 ◽

2012 ◽

Vol 157-158 ◽

pp. 652-657

Author(s):

Asma A. Shariff ◽

M. Hadi Hafezi

Keyword(s):

Maximum Likelihood ◽

Maximum Likelihood Estimation ◽

Weibull Distribution ◽

Wave Height ◽

Significant Wave Height ◽

Likelihood Estimation ◽

Rayleigh Distribution ◽

Weibull Distributions ◽

Significant Wave ◽

Two Parameter

Significant wave height is generally defined as the mean height of the highest one third of the waves in the sample and is widely regarded as an approximate equivalent to the visually observed height. Some studies assumed that wave heights can be described in terms of Log-normal, Generalized Gamma and Beta distribution, while others proposed Rayleigh distributions. In this paper, we wish to compare Rayleigh distribution with those obtained using two-parameter Weibull distributions. Both Rayleigh and Weibull distributions are used to fit the empirical data obtained from the world's oceans Global Wave Statistics. The Rayleigh distribution parameter is estimated using Maximum Likelihood Estimation (MLE) while, for the two-parameter Weibull distribution, parameter values are obtained using Maximum Likelihood Estimation and Quantile Estimation (QE). A Chi-square goodness of fit test is then used to see how the fitted distributions compare with the empirical distribution. It is found that Weibull distributions are better fits than the Rayleigh distribution, and that the MLE estimation is the best in this respect.

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Estimate Stress-Strength Reliability Model Using Rayleigh and Half-Normal Distribution

Computational Intelligence and Neuroscience ◽

10.1155/2021/7653581 ◽

2021 ◽

Vol 2021 ◽

pp. 1-10

Author(s):

Osama Abdulaziz Alamri ◽

M. M. Abd El-Raouf ◽

Eman Ahmed Ismail ◽

Zahra Almaspoor ◽

Basim S. O. Alsaedi ◽

...

Keyword(s):

Maximum Likelihood ◽

Maximum Likelihood Estimation ◽

Normal Distribution ◽

Exponential Distribution ◽

Likelihood Estimation ◽

Rayleigh Distribution ◽

Reliability Model ◽

Method Of Moment ◽

Life Testing ◽

Strength Parameters

In the field of life testing, it is very important to study the reliability of any component under testing. One of the most important subjects is the “stress-strength reliability” term which always refers to the quantity P X > Y in any statistical literature. It resamples a system with random strength (X) that is subjected to a random strength (Y) such that a system fails in case the stress exceeds the strength. In this study, we consider stress-strength reliability where the strength (X) follows Rayleigh-half-normal distribution and stress ( Y 1 , Y 2 , Y 3 , and Y 4 ) follows Rayleigh-half-normal distribution, exponential distribution, Rayleigh distribution, and half-normal distribution, respectively. This effort comprises determining the general formulations of the reliabilities of a system. Also, the maximum likelihood estimation approach and method of moment (MOM) will be utilized to estimate the parameters. Finally, reliability has been attained utilizing various values of stress and strength parameters.

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Modified maximum likelihood estimation for rayleigh distribution

Communication in Statistics- Theory and Methods ◽

10.1080/03610929608831702 ◽

1996 ◽

Vol 25 (2) ◽

pp. 389-401 ◽

Cited By ~ 19

Author(s):

S. Lalitha ◽

Anand Mishra

Keyword(s):

Maximum Likelihood ◽

Maximum Likelihood Estimation ◽

Likelihood Estimation ◽

Rayleigh Distribution ◽

Modified Maximum Likelihood

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Entropy Estimation of Inverse Weibull Distribution under Adaptive Type-II Progressive Hybrid Censoring Schemes

Symmetry ◽

10.3390/sym11121463 ◽

2019 ◽

Vol 11 (12) ◽

pp. 1463 ◽

Cited By ~ 1

Author(s):

Rong Xu and Wenhao Gui

Keyword(s):

Maximum Likelihood ◽

Maximum Likelihood Estimation ◽

Loss Function ◽

Estimation Method ◽

Likelihood Estimation ◽

Bayes Estimation ◽

Type Ii ◽

Hybrid Censoring ◽

Entropy Estimation ◽

Maximum Likelihood Estimation Method

This paper discusses entropy estimations for two-parameter inverse Weibull distributions under adaptive type-II progressive hybrid censoring schemes. Estimations of entropy derived by maximum likelihood estimation method and Bayes estimation method are both considered. Different Bayes estimators using squared loss function, Linex loss function, general entropy loss function, and balanced loss function are derived. Numerical results are derived by Lindley’s approximation method. Especially, the interval estimation of entropy is derived through maximum likelihood estimation method. To test the effectiveness of the estimations, simulation studies are conducted. These entropy estimation methods are illustrated and applied to analyze a real data set.

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