scholarly journals Bias, Precision, and Accuracy of Skewness and Kurtosis Estimators for Frequently Used Continuous Distributions

Symmetry ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 19 ◽  
Author(s):  
Roser Bono ◽  
Jaume Arnau ◽  
Rafael Alarcón ◽  
Maria J. Blanca
Keyword(s):  
Social Sciences ◽  
Monte Carlo Simulation ◽  
Sample Size ◽  
Mean Square ◽  
Exponential Distributions ◽  
Continuous Distributions ◽  
Monte Carlo Simulation Study ◽  
Normal Distributions ◽  
Precision And Accuracy ◽  
Skewness And Kurtosis

Several measures of skewness and kurtosis were proposed by Hogg (1974) in order to reduce the bias of conventional estimators when the distribution is non-normal. Here we conducted a Monte Carlo simulation study to compare the performance of conventional and Hogg’s estimators, considering the most frequent continuous distributions used in health, education, and social sciences (gamma, lognormal and exponential distributions). In order to determine the bias, precision and accuracy of the skewness and kurtosis estimators for each distribution we calculated the relative bias, the coefficient of variation, and the scaled root mean square error. The effect of sample size on the estimators is also analyzed. In addition, a SAS program for calculating both conventional and Hogg’s estimators is presented. The results indicated that for the non-normal distributions investigated, the estimators of skewness and kurtosis which best reflect the shape of the distribution are Hogg’s estimators. It should also be noted that Hogg’s estimators are not as affected by sample size as are conventional estimators.

Some Observations on the Random Response of an Elasto-Plastic System

1988 ◽  
Vol 55 (4) ◽  
pp. 911-917 ◽  
Author(s):  
L. G. Paparizos ◽  
W. D. Iwan
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Brownian Motion ◽  
Markov Process ◽  
Practical Interest ◽  
Random Excitation ◽  
Process Models ◽  
Mean Square ◽  
Random Response ◽  
Monte Carlo Simulation Study

The nature of the response of strongly yielding systems subjected to random excitation, is examined. Special attention is given to the drift response, defined as the sum of yield increments associated with inelastic response. Based on the properties of discrete Markov process models of the yield increment process, it is suggested that for many cases of practical interest, the drift can be considered as a Brownian motion. The approximate Gaussian distribution and the linearly divergent mean square value of the process, as well as an expression for the probability distribution of the peak drift response, are obtained. The validation of these properties is accomplished by means of a Monte Carlo simulation study.

Uncertainty in Stock Composition Estimates of Oceanic Steelhead Trout Using Electrophoretic Characteristics: Comments on a Recent Study

1988 ◽  
Vol 45 (3) ◽  
pp. 432-442 ◽  
Author(s):  
T. J. Mulligan ◽  
S. McKinnell ◽  
C. C. Wood
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Sample Size ◽  
Simulation Study ◽  
Recent Literature ◽  
Steelhead Trout ◽  
Monte Carlo Simulation Study ◽  
Electrophoretic Data ◽  
Mixed Stock ◽  
Insight Into

Analysis of stock composition of mixed-stock fisheries using electrophoretic data is gaining acceptance for both research and management purposes. However, a thorough understanding of the influence of sample size, stock separation, and estimation procedures is required before meaningful results can be obtained. An example from the recent literature is reanalyzed to demonstrate this conclusion. We show how widely different results are obtained from the same data when analyzed by two different models. Some insight into these differences is achieved through a Monte Carlo simulation study.

scholarly journals Performance of parametric Bayesian Methods for estimating the survivor function in uncensored data using Monte-Carlo simulation

2021 ◽  
Vol 11 (3) ◽  
pp. 430-436
Author(s):  
Mohammed Elamin Hassan ◽  
Fakhereldeen Elhaj Esmial Musa
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Maximum Likelihood ◽  
Bayesian Methods ◽  
Prior Distribution ◽  
Bayesian Method ◽  
The Other ◽  
Mean Square ◽  
Monte Carlo Simulation Study ◽  
Survivor Function

The paper aimed to investigate the performance of some parametric survivor function estimators based on Bayesian methodology with respect to bias and efficiency. A simulation was conducted based on Mote Carlo experiments with different sample sizes different (10, 30, 50, 75, 100). The bias and variance of mean square Error V(MSE) were selected as the basis of comparison. The methods of estimation used in this study are Maximum Likelihood, Bayesian with exponential as prior distribution and Bayesian with gamma as prior distribution. A Monte Carlo Simulation study showed that the Bayesian method with gamma as prior distribution was the best performance than the other methods. The study recommended that.

scholarly journals Handle outliers for Frechet distribution

2021 ◽  
Vol 23 (09) ◽  
pp. 853-863
Author(s):  
Hager Ahmad Ibrahim ◽  
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Root Mean Square Error ◽  
Mean Square Error ◽  
Simulation Study ◽  
Mean Square ◽  
Monte Carlo Simulation Study ◽  
Fréchet Distribution ◽  
Outlier Data ◽  
Frechet Distribution

This paper aims to handle outlier data for Frechet distribution. This study focused on two ways to deal with outliers. The rst way is to censor the ob- servation with the same percentage of outlier data. The second way is to trim outlier observations. A Monte Carlo simulation study is carried out to compare these ways in terms of estimate average, relative bias, and root mean square error (RMSE) using Mathematica-10.

scholarly journals Normality for Non-normal Distributions

2020 ◽  
Vol 8 (2) ◽  
pp. 51-60
Author(s):  
Khong Liang Koh ◽  
Nor Aishah Ahad
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Sample Size ◽  
Computer Simulations ◽  
General Rule ◽  
Exponential Distributions ◽  
Normal Distributions ◽  
Normality Assumption ◽  
Gamma Distributions ◽  
Sample Data

It has been usually assumed that a sample data is normally distributed when the sample size is at least 30. This is the general rule in using central limit theorem based on the sample size being greater or equal to 30. Many literary works also assumed normality when sample size is at least 30. This study aims to determine the least required sample size that satisfy normality assumption from three non-normal distributions, Poisson, Gamma and Exponential distributions. Computer simulations are carried out to study the least required sample size for the three distributions. Through the study, it is found that sample data from Poisson and Gamma distributions need sample size less than 30, while Exponential needs more than 30 to achieve normality.

Sign in / Sign up

Export Citation Format

Share Document