Birdal Şenoğlu

A comparative study for the location and scale parameters of the Weibull distribution with given shape parameter

Nine parametric estimators of the location and scale parameters of a two-parameter Weibull distribution are compared in terms of their bias and efficiency in a simulation study. The estimators considered are the maximum likelihood estimators (MLE), moment estimators (ME), generalized spacing estimators (GSE), modified maximum likelihood estimators I (MMLE-I), modified maximum likelihood estimators II (MMLE-II), Tikus modified maximum likelihood estimators (TMMLE), least-squares estimators (LSE), weighted least-squares estimators (WLSE) and percentile estimators (PCE). The aim of the comparisons is to identify the most efficient estimators among these nine estimators for different shape parameters and sample sizes.

ANALYSIS OF VARIANCE IN EXPERIMENTAL DESIGN WITH NONNORMAL ERROR DISTRIBUTIONS

We consider a two-way classification model with interaction and assume that the errors have a location-scale nonnormal distribution. From an application of the modified likelihood estimation, we obtain efficient and robust estimators of the parameters. We define F statistics for testing main effects and interaction. We analyze the Box-Cox data and show that the method developed in this paper gives accurate results besides being easy theoretically and computationally.

Linear Contrasts in Experimental Design with Non‐Identical Error Distributions

Estimation of linear contrasts in experimental design, and testing their assumed values, is considered when the error distributions from block to block are not necessarily identical. The normal-theory solutions are shown to have low efficiencies as compared to the solutions presented here.

Comparison of certain value-at-risk estimation methods for the two-parameter Weibull loss distribution

The Weibull distribution is one of the most important distributions that is utilized as a probability model for loss amounts in connection with actuarial and financial risk management problems. This paper considers the Weibull distribution and its quantiles in the context of estimation of a risk measure called Value-at-Risk (VaR). VaR is simply the maximum loss in a specified period with a pre-assigned probability level. We attempt to present certain estimation methods for VaR as a quantile of a distribution and compare these methods with respect to their deficiency (Def) values. Along this line, the results of some Monte Carlo simulations, that we have conducted for detailed investigations on the efficiency of the estimators as compared to MLE, are provided.

Effects of Physical Environment on the Stress Levels of Hemodialysis Nurses in Ankara Turkey

This study has been planned and executed as a field study for identifying the effect of physical environment on the stress levels of hemodialysis nurses who work in the official and private hemodialysis centers in the capital city of Turkey, Ankara (n = 161). According to the results obtained from the study, it has been seen that “education level” and “institution of employment” of the hemodialysis nurses are significantly related with the stress levels of the hemodialysis nurses. Nurses’ age, marital status, number of children, occupational seniority, years of working, employment status, husbands’ occupation and husbands’ educational levels are not significantly related with their stress levels.

Evaluation of surface water quality characteristics by using multivariate statistical techniques: a case study of the Euphrates river basin, Turkey.

The surface water quality of the Euphrates river basin in Turkey are evaluated by using the multivariate statistical techniques known as factor analysis (FA) and multidimensional scaling (MDS) analysis. When FA was applied to the water quality data obtained from the 15 different surface water quality monitoring stations, two factors were identified, which were responsible from the 86.02% of the total variance of the water quality in the Euphrates river basin. The first factor called the urban land use factor explained 44.20% of the total variance and the second factor called the agricultural use factor explained 41.81% of the total variance. MDS technique showed that electrical conductivity (EC), percent sodium (Na%) and total salt are the most important variables causing difference in the water quality analysis.

Parameter estimation in geometric process with Weibull distribution

We consider geometric process (GP) when the distribution of the first occurrence time of an event is assumed to be Weibull. Explicit estimators of the parameters in GP are derived by using the method of modified maximum likelihood (MML) proposed by Tiku [24]. Asymptotic distributions and consistency properties of these estimators are obtained. We show that our estimators are more efficient than the widely used modified moment (MM) estimators via Monte Carlo simulation study. Further, two real life examples are given at the end of the paper.

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.

Estimation of P(X < Y) using ranked set sampling for the Weibull distribution

Abstract This paper deals with making inferences regarding system reliability when the distribution of the stress X and the strength Y are independent Weibull. In the literature, estimators based on simple random sampling (SRS) are widely used in estimating R. However, in recent years, ranked set sampling (RSS) has become popular in performing statistical inference. We, therefore, obtain the estimators of R based on RSS using maximum likelihood (ML) and modified maximum likelihood (MML) methodologies. The performances of the proposed estimators are compared with their counterparts based on SRS using Monte Carlo simulation. The simulation results show that the proposed estimators are more preferable than the estimators based on SRS in terms of efficiency. In addition, under the assumption of imperfect ranking the efficiencies of the ML and the MML estimators of R, based on RSS, are compared and the ML estimator of R is found to be more efficient. Finally, a real data-set is analysed to demonstrate the implementation of the proposed estimators at the end of the paper.

Statistical inference for α-series process with gamma distribution

ABSTRACT The explicit estimators of the parameters α, μ and σ2 are obtained by using the methodology known as modified maximum likelihood (MML) when the distribution of the first occurrence time of an event is assumed to be Weibull in series process. The efficiencies of the MML estimators are compared with the corresponding nonparametric (NP) estimators and it is shown that the proposed estimators have higher efficiencies than the NP estimators. In this study, we extend these results to the case, where the distribution of the first occurrence time is Gamma. It is another widely used and well-known distribution in reliability analysis. A real data set taken from the literature is analyzed at the end of the study for better understanding the methodology presented in this paper.