scholarly journals Bayesian Estimation of the Parameter of the p-Dimensional Size-Biased Rayleigh Distribution

2017 ◽  
Vol 56 (1) ◽  
pp. 88-91
Author(s):  
Arun Kumar Rao ◽  
Himanshu Pandey ◽  
Kusum Lata Singh
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Bayesian Estimation ◽  
Density Function ◽  
Rayleigh Distribution ◽  
Survival Model ◽  
Loss Functions ◽  
Bayes Estimators ◽  
Hazard Functions ◽  
Squared Error

In this paper, we have derived the probability density function of the size-biased p-dimensional Rayleigh distribution and studied its properties. Its suitability as a survival model has been discussed by obtaining its survival and hazard functions. We also discussed Bayesian estimation of the parameter of the size-biased p-dimensional Rayleigh distribution. Bayes estimators have been obtained by taking quasi-prior. The loss functions used are squared error and precautionary.

scholarly journals Bayesian Estimation of Exponentiated Inverse Rayleigh Distribution

2021 ◽  
Vol 9 (03) ◽  
pp. 321-328
Author(s):  
Arun Kumar Rao ◽  
Himanshu Pandey
Keyword(s):  
Bayesian Analysis ◽  
Bayesian Estimation ◽  
Rayleigh Distribution ◽  
Loss Functions ◽  
Bayes Estimators ◽  
Squared Error

In this paper, exponentiated inverse Rayleigh distribution is considered for Bayesian analysis. The expressions for Bayes estimators of the parameter have been derived under squared error, precautionary, entropy, K-loss, and Al-Bayyati’s loss functions by using quasi and gamma priors.

scholarly journals Estimation of Survival Function for Rayleigh Distribution by Ranking function:-

2019 ◽  
Vol 16 (3(Suppl.)) ◽  
pp. 0775
Author(s):  
Hussein Et al.
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Scale Parameter ◽  
Survival Function ◽  
Rayleigh Distribution ◽  
Ordinary Least Squares ◽  
Ranking Functions ◽  
Hazard Functions ◽  
Ordinary Least Squares Estimator

In this article, performing and deriving te probability density function for Rayleigh distribution is done by using ordinary least squares estimator method and Rank set estimator method. Then creating interval for scale parameter of Rayleigh distribution. Anew method using   is used for fuzzy scale parameter. After that creating the survival and hazard functions for two ranking functions are conducted to show which one is beast.

scholarly journals With Bayesian Estimation One Can Get All That Bayes Factors Offer, and More

2019 ◽  
Author(s):  
Henk Kiers ◽  
Jorge Tendeiro
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Bayesian Estimation ◽  
Density Function ◽  
Null Hypothesis ◽  
Posterior Odds ◽  
Close Link ◽  
Posterior Odds Ratio ◽  
Spike And Slab Prior ◽  
Point Null Hypothesis

Null Hypothesis Bayesian Testing (NHBT) has been proposed as an alternative to Null Hypothesis Significance Testing (NHST). Whereas NHST has a close link to parameter estimation via confidence intervals, such a link of NHBT with Bayesian estimation via a posterior distribution is less straightforward, but does exist, and has recently been reiterated by Rouder, Haaf, and Vandekerckhove (2018). It hinges on a combination of a point mass probability and a probability density function as prior (denoted as the spike-and-slab prior). In the present paper it is first carefully explained how the spike-and-slab prior is defined, and how results can be derived for which proofs were not given in Rouder et al. (2018). Next, it is shown that this spike-and-slab prior can be approximated by a pure probability density function with a rectangular peak around the center towering highly above the remainder of the density function. Finally, we will indicate how this ‘hill-and-chimney’ prior may in turn be approximated by fully continuous priors. In this way it is shown that NHBT results can be approximated well by results from estimation using a strongly peaked prior, and it is noted that the estimation itself offers more than merely the posterior odds ratio on which NHBT is based. Thus, it complies with the strong APA requirement of not just mentioning testing results but also offering effect size information. It also offers a transparent perspective on the NHBT approach employing a prior with a strong peak around the chosen point null hypothesis value.

scholarly journals Distributions in Life Insurance

1990 ◽  
Vol 20 (1) ◽  
pp. 81-92 ◽  
Author(s):  
Jan Dhaene
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Life Insurance ◽  
Wide Class ◽  
Stochastic Theory ◽  
Stochastic Approach ◽  
Higher Order ◽  
Loss Functions ◽  
Higher Order Moments

AbstractIn most textbooks and papers that deal with the stochastic theory of life contingencies, the stochastic approach is restricted to the computation of expectations and higher order moments. For a wide class of insurances on a single life, we derive the distribution and the probability density function of the benefit and the loss functions. Both the continuous and the discrete case are considered.

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