Monte Carlo Comparison of the Parameter Estimation Methods for the Two-Parameter Gumbel Distribution

The performances of the seven different parameter estimation methods for the Gumbel distribution are compared with numerical simulations. Estimation methods used in this study are the method of moments (ME), the method of maximum likelihood (ML), the method of modified maximum likelihood (MML), the method of least squares (LS), the method of weighted least squares (WLS), the method of percentile (PE) and the method of probability weighted moments (PWM). Performance of the estimators is compared with respect to their biases, MSE and deficiency (Def) values via Monte-Carlo simulation. A Monte Carlo Simulation study showed that the method of PWM was the best performance the other methods of bias criterion and the method of ML outperforms the other methods in terms of Def criterion. A real life example taken from the hydrology literature is given at the end of the paper

Inference for the jones and faddy's skewed t-distribution based on progressively type-II censored samples

In this paper, the location and the scale parameters of Jones and Faddy’s skewed t (JFST) distribution are estimated based on progressively Type-II censored samples. We obtain maximum likelihood (ML) and modified maximum likelihood (MML) estimators of unknown parameters. Then, confidence intervals for the estimators of μ and σ are obtained. The performances of proposed methodologies are compared via Monte-Carlo simulation study. It is concluded that the ML and MML estimators are close, especially for moderate and large sample sizes. At the end of the study, real life data is analyzed for illustrative proposes

A Monte Carlo Comparison of Regression Estimators When the Error Distribution is Long-Tailed Symmetric

The performances of the ordinary least squares (OLS), modified maximum likelihood (MML), least absolute deviations (LAD), Winsorized least squares (WIN), trimmed least squares (TLS), Theil’s (Theil) and weighted Theil’s (Weighted Theil) estimators are compared under the simple linear regression model in terms of their bias and efficiency when the distribution of error terms is long-tailed symmetric

Estimation of the location and the scale parameters of Burr Type XII distribution

The aim of this paper is to estimate the location and the scale parameters of Burr Type XII distribution. For this purpose, different estimation methods, namely, maximum likelihood (ML), modified maximum likelihood (MML), least squares (LS) and method of moments (MM) are used. The performances of these estimation methods are compared via Monte-Carlo simulation study under different sample sizes and parameter settings. At the end of the study, the wind speed data set and the annual flow data sets are analyzed for illustration of the modeling performance of Burr Type XII distribution

Interval estimation of the system reliability for Weibull distribution based on ranked set sampling data

Inference for the system reliability R is one of the most popular problems in the areas of engineering, statistics, biostatistics and etc. Therefore, there exist considerable numbers of studies concerning this problem. Traditionally, simple random sampling (SRS) is used for estimating the system reliability. However, in recent years, ranked set sampling (RSS), cost effective and efficient alternative of SRS, is used to estimate the system reliability. In this study, we consider the interval estimation of R when both the stress and the strength are independent Weibull random variables based on RSS. We first obtain the asymptotic confidence interval (ACI) of R by using the maximum likelihood (ML) methodology. The bootstrap confidence interval (BCI) of R is also constructed as an alternative to ACI. An extensive Monte-Carlo simulation study is conducted to compare the performances of ACI and BCI of R for different settings. Finally, a real data set is analyzed to demonstrate the implementation of the proposed methods

Robust estimation of the location and the scale parameters of shifted Gompertz distribution

In this study, we consider the estimation of the location parameter  and the scale parameter  of the shifted Gompertz (SG) distribution. We obtain the closed form estimators of these parameters by using the modified maximum likelihood (MML) methodology originated by Tiku (1967). We also compare the efficiencies of these estimators with the well-known and widely used least squares (LS) and maximum likelihood (ML) estimators via Monte-Carlo simulation study in terms of bias, mean square error (MSE) and deficiency (Def) criteria. In addition, we evaluate the performances of the proposed estimators when the data contains the outliers or is contaminated. In other words, the robustness properties of the estimators are investigated. A real data set is analyzed to demonstrate the implementation of the estimation methods at the end of the study

Experimental design under nonnormality

Ph.D. - Doctoral Progra

ÇİFT TARAFLI TİP II SANSÜRLENMİŞ ÖRNEKLEMLER İÇİN JONES VE FADDY’ NİN ÇARPIK t DAĞILIMININ KONUM VE ÖLÇEK PARAMETRELERİNİN TAHMİNİ

Bu çalışmada, çift taraflı Tip II sansürlenmiş (doubly Type II censored) örneklemler için Jones ve Faddy’ nin çarpık t (Jones and Faddy’ s Skew t - JFST) dağılımının konum ve ölçek parametrelerinin en çok olabilirlik (maximum likelihood - ML) ve uyarlanmış en çok olabilirlik (modified maximum likelihood - MML) tahmin edicileri elde edilmiştir. Monte Carlo (MC) simülasyon çalışması kullanılarak ML ve MML tahmin edicilerinin etkinlikleri karşılaştırılmıştır. MC simülasyon çalışması, MML tahmin edicilerinin ML tahmin edicileri ile hemen hemen aynı etkinliğe sahip olduğunu göstermiştir. Çalışma sonucunda, odaklanılan nokta tahmin edicilerin etkinlikleri ise ML tahmin edicilerinin, etkinlikle beraber hesaplama zorlukları ele alındığında ise MML tahmin edicilerinin tercih edilmesi gerektiği belirlenmiştir

Estimation and hypothesis testing in BIB design and robustness

Modified maximum likelihood estimators of the unknown parameters in a BIB design under non-normality of error distributions are obtained. They are shown to be more efficient and robust than the traditional least squares estimators. A test statistic for testing a linear contrast among treatment effects is developed. A real life example is given