scholarly journals Classical and Bayesian Approach in Estimation of Scale Parameter of Nakagami Distribution

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Kaisar Ahmad ◽  
S. P. Ahmad ◽  
A. Ahmed
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Bayesian Approach ◽  
Simulation Study ◽  
Bayesian Method ◽  
Scale Parameter ◽  
Loss Functions ◽  
Likelihood Estimator ◽  
R Software ◽  
Nakagami Distribution

Nakagami distribution is considered. The classical maximum likelihood estimator has been obtained. Bayesian method of estimation is employed in order to estimate the scale parameter of Nakagami distribution by using Jeffreys’, Extension of Jeffreys’, and Quasi priors under three different loss functions. Also the simulation study is conducted in R software.

scholarly journals Transforming variables to central normality

2021 ◽  
Author(s):  
Jakob Raymaekers ◽  
Peter J. Rousseeuw
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Simulation Study ◽  
Real Data ◽  
Data Sets ◽  
Transformation Parameter ◽  
Likelihood Estimator ◽  
Extensive Simulation ◽  
Highly Sensitive

AbstractMany real data sets contain numerical features (variables) whose distribution is far from normal (Gaussian). Instead, their distribution is often skewed. In order to handle such data it is customary to preprocess the variables to make them more normal. The Box–Cox and Yeo–Johnson transformations are well-known tools for this. However, the standard maximum likelihood estimator of their transformation parameter is highly sensitive to outliers, and will often try to move outliers inward at the expense of the normality of the central part of the data. We propose a modification of these transformations as well as an estimator of the transformation parameter that is robust to outliers, so the transformed data can be approximately normal in the center and a few outliers may deviate from it. It compares favorably to existing techniques in an extensive simulation study and on real data.

Shape averages and their Bias

1994 ◽  
Vol 26 (2) ◽  
pp. 334-340 ◽  
Author(s):  
K. V. Mardia ◽  
I. L. Dryden
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Simulation Study ◽  
Normal Model ◽  
Likelihood Estimator ◽  
Distributional Properties ◽  
Exact Maximum Likelihood

The paper considers the bias of Bookstein's mean estimator for shape under the isotropic normal model. This work depends on certain distributional properties of shape variables. An alternative unbiased modified estimator is proposed and its performance is compared with various estimators, including Procrustes and the exact maximum likelihood estimator, in a simulation study.

A mutual information estimator with exponentially decaying bias

2015 ◽  
Vol 14 (3) ◽  
Author(s):  
Zhiyi Zhang ◽  
Lukun Zheng
Keyword(s):  
Maximum Likelihood ◽  
Mutual Information ◽  
Asymptotic Normality ◽  
Sample Size ◽  
Maximum Likelihood Estimator ◽  
Simulation Study ◽  
Type I Error ◽  
Type I ◽  
Nonparametric Estimator ◽  
Likelihood Estimator

AbstractA nonparametric estimator of mutual information is proposed and is shown to have asymptotic normality and efficiency, and a bias decaying exponentially in sample size. The asymptotic normality and the rapidly decaying bias together offer a viable inferential tool for assessing mutual information between two random elements on finite alphabets where the maximum likelihood estimator of mutual information greatly inflates the probability of type I error. The proposed estimator is illustrated by three examples in which the association between a pair of genes is assessed based on their expression levels. Several results of simulation study are also provided.

scholarly journals Estimation of P{X < Y} for gamma exponential model

2014 ◽  
Vol 24 (2) ◽  
pp. 283-291 ◽  
Author(s):  
Milan Jovanovic ◽  
Vesna Rajic
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Exponential Distribution ◽  
Asymptotic Distribution ◽  
Simulation Study ◽  
Random Variables ◽  
Exponential Model ◽  
Independent Random Variables ◽  
Likelihood Estimator

In this paper, we estimate probability P{X < Y} when X and Y are two independent random variables from gamma and exponential distribution, respectively. We obtain maximum likelihood estimator and its asymptotic distribution. We perform some simulation study.

scholarly journals Estimation of Reliability for a Two Component Survival Stress-Strength Model

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
S. B. Munoli ◽  
Rohit R. Mutkekar
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Simulation Study ◽  
Maximum Likelihood Estimators ◽  
Reliability Function ◽  
Strength Model ◽  
Life Testing ◽  
Likelihood Estimator ◽  
Two Component ◽  
Testing Experiment

The reliability function for a parallel system of two identical components is derived from a stress-strength model, where failure of one component increases the stress on the surviving component of the system. The Maximum Likelihood Estimators of parameters and their asymptotic distribution are obtained. Further the Maximum Likelihood Estimator and Bayes Estimator of reliability function are obtained using the data from a life-testing experiment. Computation of estimators is illustrated through simulation study.

A SIMPLE ESTIMATOR FOR THE WEIBULL SHAPE PARAMETER

2012 ◽  
Vol 12 (02) ◽  
pp. 395-402 ◽  
Author(s):  
MAHDI TEIMOURI ◽  
SARALEES NADARAJAH
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Closed Form ◽  
Maximum Likelihood Estimator ◽  
Shape Parameter ◽  
Scale Parameter ◽  
Maximum Likelihood Estimators ◽  
Simulation Studies ◽  
Likelihood Estimator

The Weibull distribution is the most popular model for lifetimes. However, the maximum likelihood estimators for the Weibull distribution are not available in closed form. In this note, we derive a simple, consistent, closed form estimator for the Weibull shape parameter. This estimator is independent of the Weibull scale parameter. Simulation studies show that this estimator performs as well as the maximum likelihood estimator.

Estimation in truncated Poisson distribution

2011 ◽  
Vol 61 (2) ◽  
Author(s):  
Khurshid Mir
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Poisson Distribution ◽  
Recurrence Relations ◽  
Bayes Estimator ◽  
Likelihood Estimator ◽  
R Software

AbstractBayes’ estimator of truncated Poisson distribution (TPD) has been obtained by using gamma prior. Furthermore, recurrence relations for the estimator of the parameter are obtained. R-software has been used for comparing the estimates with the corresponding maximum likelihood estimator (MLE).

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