scholarly journals Modified Moments and Maximum Likelihood Estimators for Parameters of Erlang Truncated Exponential Distribution

2021 ◽  
pp. 34-37
Author(s):  
Kannadasan Karuppaiah ◽  
◽  
Vinoth Raman ◽  
Keyword(s):  
Maximum Likelihood ◽  
Exponential Distribution ◽  
Method Of Moments ◽  
Scale Parameter ◽  
Likelihood Function ◽  
Continuous Distribution ◽  
Regression Estimators ◽  
Mean And Variance ◽  
Mathematical Derivation ◽  
Modified Moments

This study derives the parameter estimation in truncated form of a continuous distribution which is comparable to Erlang truncated exponential distribution. The shape and scale parameter will predict the whole distributions properties. Approximation will be useful in making the mathematical calculation an easy understand for non-mathematician or statistician. An explicit mathematical derivation is seen for some properties of, Method of Moments, Skewness, Kurtosis, Mean and Variance, Maximum Likelihood Function and Reliability Analysis. We compared ratio and regression estimators empirically based on bias and coefficient of variation.

scholarly journals Modified Moments and Maximum Likelihood Estimators for Parameters of Erlang Truncated Exponential Distribution

2021 ◽  
Vol 1 (1) ◽  
pp. 34-37
Author(s):  
Kannadasan Karuppaiah ◽  
Vinoth Raman
Keyword(s):  
Maximum Likelihood ◽  
Exponential Distribution ◽  
Method Of Moments ◽  
Scale Parameter ◽  
Likelihood Function ◽  
Continuous Distribution ◽  
Regression Estimators ◽  
Mean And Variance ◽  
Mathematical Derivation ◽  
Modified Moments

This study derives the parameter estimation in truncated form of a continuous distribution which is comparable to Erlang truncated exponential distribution. The shape and scale parameter will predict the whole distributions properties. Approximation will be useful in making the mathematical calculation an easy understand for non-mathematician or statistician. An explicit mathematical derivation is seen for some properties of, Method of Moments, Skewness, Kurtosis, Mean and Variance, Maximum Likelihood Function and Reliability Analysis. We compared ratio and regression estimators empirically based on bias and coefficient of variation.

scholarly journals Shrinkage Estimators for the Exponential Scale Parameter under Multiply Type II Censoring

2016 ◽  
Vol 34 (1) ◽  
Author(s):  
Umesh Singh ◽  
Anil Kumar
Keyword(s):  
Maximum Likelihood ◽  
Exponential Distribution ◽  
Scale Parameter ◽  
Maximum Likelihood Estimators ◽  
Shrinkage Estimators ◽  
Type Ii ◽  
Approximate Maximum Likelihood ◽  
Type Ii Censoring ◽  
Mean Squared Errors

We consider the problem of estimating the scale parameter of an exponential distribution under multiply type II censoring when a prior point guess of the parameter value is available. Shrinkage estimators are obtained from the approximate maximum likelihood estimators proposed in Singh et al. (2004) and in Balasubramanian and Balakrishnan (1992). These estimators are then compared by their simulated mean squared errors.

scholarly journals Multigeneration Maximum-Likelihood Analysis Applied to Mutation-Accumulation Experiments in Caenorhabditis elegans

Genetics ◽  
2000 ◽  
Vol 154 (3) ◽  
pp. 1193-1201 ◽  
Author(s):  
Peter D Keightley ◽  
Thomas M Bataillon
Keyword(s):  
Caenorhabditis Elegans ◽  
Maximum Likelihood ◽  
Method Of Moments ◽  
Mutation Accumulation ◽  
Life History Trait ◽  
Homozygous Mutation ◽  
C Elegans ◽  
Likelihood Analysis ◽  
Mean And Variance ◽  
Rule Out

AbstractWe develop a maximum-likelihood (ML) approach to estimate genomic mutation rates (U) and average homozygous mutation effects (s) from mutation-accumulation (MA) experiments in which phenotypic assays are carried out in several generations. We use simulations to compare the procedure's performance with the method of moments traditionally used to analyze MA data. Similar precision is obtained if mutation effects are small relative to the environmental standard deviation, but ML can give estimates of mutation parameters that have lower sampling variances than those obtained by the method of moments if mutations with large effects have accumulated. The inclusion of data from intermediate generations may improve the precision. We analyze life-history trait data from two Caenorhabditis elegans MA experiments. Under a model with equal mutation effects, the two experiments provide similar estimates for U of ~0.005 per haploid, averaged over traits. Estimates of s are more divergent and average at −0.51 and −0.13 in the two studies. Detailed analysis shows that changes of mean and variance of genetic values of MA lines in both C. elegans experiments are dominated by mutations with large effects, but the analysis does not rule out the presence of a large class of deleterious mutations with very small effects.

scholarly journals Maximum observed likelihood prediction of future record values

Test ◽  
2020 ◽  
Vol 29 (4) ◽  
pp. 1072-1097 ◽  
Author(s):  
Grigoriy Volovskiy ◽  
Udo Kamps
Keyword(s):  
Maximum Likelihood ◽  
Mean Squared Error ◽  
Likelihood Function ◽  
Continuous Distribution ◽  
Record Values ◽  
Extreme Value ◽  
Cumulative Distribution ◽  
Performance Criteria ◽  
Upper Record Values ◽  
Upper Record

AbstractPoint prediction of future upper record values is considered. For an underlying absolutely continuous distribution with strictly increasing cumulative distribution function, the general form of the predictor obtained by maximizing the observed predictive likelihood function is established. The results are illustrated for the exponential, extreme-value and power-function distributions, and the performance of the obtained predictors is compared to that of maximum likelihood predictors on the basis of the mean squared error and the Pitman’s measure of closeness criteria. For exponential and extreme-value distributions, it is shown that under slight restrictions, the maximum observed likelihood predictor outperforms the maximum likelihood predictor in terms of both performance criteria.

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

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.

scholarly journals Generalized Modified Slash Birnbaum–Saunders Distribution

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 724 ◽  
Author(s):  
Jimmy Reyes ◽  
Inmaculada Barranco-Chamorro ◽  
Diego Gallardo ◽  
Héctor Gómez
Keyword(s):  
Maximum Likelihood ◽  
Em Algorithm ◽  
Standard Normal Distribution ◽  
Stochastic Representation ◽  
Moments Method ◽  
Standard Normal ◽  
Newton Raphson ◽  
New Distribution ◽  
Skewness And Kurtosis ◽  
Modified Moments

In this paper, a generalization of the modified slash Birnbaum–Saunders (BS) distribution is introduced. The model is defined by using the stochastic representation of the BS distribution, where the standard normal distribution is replaced by a symmetric distribution proposed by Reyes et al. It is proved that this new distribution is able to model more kurtosis than other extensions of BS previously proposed in the literature. Closed expressions are given for the pdf (probability density functio), along with their moments, skewness and kurtosis coefficients. Inference carried out is based on modified moments method and maximum likelihood (ML). To obtain ML estimates, two approaches are considered: Newton–Raphson and EM-algorithm. Applications reveal that it has potential for doing well in real problems.

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