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.

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.

scholarly journals Robustness Test of Selected Estimators of Linear Regression with Autocorrelated Error Term: A Monte-Carlo Simulation Study

2021 ◽  
pp. 1-17
Author(s):  
Rauf Ibrahim Rauf ◽  
Okoli Juliana Ifeyinwa ◽  
Haruna Umar Yahaya
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Maximum Likelihood ◽  
Linear Regression ◽  
Simulation Study ◽  
Explanatory Variable ◽  
Real Life ◽  
Least Square ◽  
Monte Carlo Simulation Study ◽  
Error Terms

Assumptions in the classical linear regression model include that of lack of autocorrelation of the error terms and the zero covariance between the explanatory variable and the error terms. This study is channeled towards the estimation of the parameters of the linear models for both time series and cross-sectional data when the above two assumptions are violated. The study used the Monte-Carlo simulation method to investigate the performance of six estimators: ordinary least square (OLS), Prais-Winsten (PW), Cochrane-Orcutt (CC), Maximum Likelihood (MLE), Restricted Maximum- Likelihood (RMLE) and the Weighted Least Square (WLS) in estimating the parameters of a single linear model in which the explanatory variable is also correlated with the autoregressive error terms. Using the models’ finite properties(mean square error) to measure the estimators’ performance, the results shows that OLS should be preferred when autocorrelation level is relatively mild (ρ = 0.3) and the PW, CC, RMLE, and MLE estimator will perform better with the presence of any level of AR (1) disturbance between 0.4 to 0.8 level, while WLS shows better performance at 0.9 level of autocorrelation and above. The study thus recommended the application of the various estimators considered to real-life data to affirm the results of this simulation study.

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 TL-Moments for Type-I Censored Data with an Application to the Weibull Distribution

2018 ◽  
Author(s):  
Hager A. Ibrahim ◽  
Mahmoud Riad Mahmoud ◽  
Fatma A. Khalil ◽  
Ghada A. El-Kelany
Keyword(s):  
Monte Carlo Simulation ◽  
Weibull Distribution ◽  
Censored Data ◽  
The Other ◽  
Type I ◽  
Mean Square ◽  
Unknown Parameters ◽  
Monte Carlo Simulation Study ◽  
Moments Method ◽  
L Moments

This paper aims to provide an adaptation of the TL-moments method to censored data. The present study concentrates on Type-I censored data. The idea of using TL-moments with censored data may seem conflicting. But our perspective in that, we may use data censored from one side and trimmed from the other side. This study is applied to estimate the two unknown parameters of the Weibull distribution. The suggested point is compared with Direct L-moments and ML methods. A Monte Carlo simulation study is carried out to compare these method in terms of estimate average, root of mean square error (RMSE) and relative absolute biases (RAB).

scholarly journals Applying the rescaling bootstrap under imputation for a multistage sampling design

2021 ◽  
Author(s):  
Christian Bruch
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Simulation Study ◽  
Missing Values ◽  
Sampling Design ◽  
The Other ◽  
Original Version ◽  
Monte Carlo Simulation Study ◽  
Resampling Method ◽  
Multistage Sampling

AbstractIn this paper, we propose a method that estimates the variance of an imputed estimator in a multistage sampling design. The method is based on the rescaling bootstrap for multistage sampling introduced by Preston (Surv Methodol 35(2):227–234, 2009). In his original version, this resampling method requires that the dataset includes only complete cases and no missing values. Thus, we propose two modifications for applying this method to nonresponse and imputation. These modifications are compared to other modifications in a Monte Carlo simulation study. The results of our simulation study show that our two proposed approaches are superior to the other modifications of the rescaling bootstrap and, in many situations, produce valid estimators for the variance of the imputed estimator in multistage sampling designs.

A bivariate Pareto type I models

2017 ◽  
Vol 5 (1) ◽  
pp. 44
Author(s):  
Mervat Abd Elaal ◽  
Hind Alzahrani
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Maximum Likelihood ◽  
Simulation Study ◽  
Real Data ◽  
Type I ◽  
Data Set ◽  
Monte Carlo Simulation Study ◽  
Bayesian Estimations

In this paper two new bivariate Pareto Type I distributions are introduced. The first distribution is based on copula, and the second distribution is based on mixture of and copula. Maximum likelihood and Bayesian estimations are used to estimate the parameters of the proposed distribution. A Monte Carlo Simulation study is carried out to study the behavior of the proposed distributions. A real data set is analyzed to illustrate the performance and flexibility of the proposed distributions.

scholarly journals TL-Moments for Type-I Censored Data with an Application to the Weibull Distribution

2018 ◽  
Vol 23 (3) ◽  
pp. 47
Author(s):  
Hager Ibrahim ◽  
Mahmoud Mahmoud ◽  
Fatma Khalil ◽  
Ghada El-Kelany
Keyword(s):  
Monte Carlo Simulation ◽  
Weibull Distribution ◽  
Censored Data ◽  
The Other ◽  
Type I ◽  
Mean Square ◽  
Unknown Parameters ◽  
Monte Carlo Simulation Study ◽  
Moments Method ◽  
L Moments

This paper aims to provide an adaptation of the trimmed L (TL)-moments method to censored data. The present study concentrates on Type-I censored data. The idea of using TL-moments with censored data may seem conflicting. However, our perspective is that we can use data censored from one side and trimmed from the other side. This study is applied to estimate the two unknown parameters of the Weibull distribution. The suggested point is compared with direct L-moments and maximum likelihood (ML) methods. A Monte Carlo simulation study is carried out to compare these methods in terms of estimate average, root of mean square error (RMSE), and relative absolute biases (RABs).

scholarly journals The Analysis for the Recovery Cases of COVID-19 in Egypt using Odd Generalized Exponential Lomax Distribution

2021 ◽  
pp. 52-65
Author(s):  
Hanem Mohamed ◽  
Amina E. Abo-Hussien ◽  
Salwa A. Mousa ◽  
Magda M. Ismail
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Maximum Likelihood ◽  
Confidence Intervals ◽  
The Other ◽  
Model Parameters ◽  
Practical Applications ◽  
Mathematical Properties ◽  
Proposed Model ◽  
Asymptotic Confidence Intervals

In this paper, an odd generalized exponential Lomax (OGEL, in short) distribution has been considered. Some mathematical properties of the distribution are studied. The methods of maximum likelihood and maximum product of spacing are used for estimating the model parameters.  Moreover, 95% asymptotic confidence intervals for the estimates of the parameters are derived. The Monte Carlo simulation is conducted for the two proposed methods of estimation to evaluate the performance of the various proposed estimators. The proposed methods are utilized to find estimates of the parameters of OGEL distribution for the daily recovery cases of COIVD-19 in Egypt from 12 May to 30 September 2020.The practical applications show that the proposed model provides better fits than the other models.

Bayesian Applications in Auditory Research

2019 ◽  
Vol 62 (3) ◽  
pp. 577-586 ◽  
Author(s):  
Garnett P. McMillan ◽  
John B. Cannon
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Bayesian Methods ◽  
Prior Distribution ◽  
Interim Analysis ◽  
Iterative Process ◽  
Bayes Theorem ◽  
Sound Therapy ◽  
The Many ◽  
Auditory Research

Purpose This article presents a basic exploration of Bayesian inference to inform researchers unfamiliar to this type of analysis of the many advantages this readily available approach provides. Method First, we demonstrate the development of Bayes' theorem, the cornerstone of Bayesian statistics, into an iterative process of updating priors. Working with a few assumptions, including normalcy and conjugacy of prior distribution, we express how one would calculate the posterior distribution using the prior distribution and the likelihood of the parameter. Next, we move to an example in auditory research by considering the effect of sound therapy for reducing the perceived loudness of tinnitus. In this case, as well as most real-world settings, we turn to Markov chain simulations because the assumptions allowing for easy calculations no longer hold. Using Markov chain Monte Carlo methods, we can illustrate several analysis solutions given by a straightforward Bayesian approach. Conclusion Bayesian methods are widely applicable and can help scientists overcome analysis problems, including how to include existing information, run interim analysis, achieve consensus through measurement, and, most importantly, interpret results correctly. Supplemental Material https://doi.org/10.23641/asha.7822592

Sign in / Sign up

Export Citation Format

Share Document