Kyeongjun Lee

Estimating the Entropy of a Weibull Distribution under Generalized Progressive Hybrid Censoring

Recently, progressive hybrid censoring schemes have become quite popular in a life-testing problem and reliability analysis. However, the limitation of the progressive hybrid censoring scheme is that it cannot be applied when few failures occur before time T. Therefore, a generalized progressive hybrid censoring scheme was introduced. In this paper, the estimation of the entropy of a two-parameter Weibull distribution based on the generalized progressively censored sample has been considered. The Bayes estimators for the entropy of the Weibull distribution based on the symmetric and asymmetric loss functions, such as the squared error, linex and general entropy loss functions, are provided. The Bayes estimators cannot be obtained explicitly, and Lindley’s approximation is used to obtain the Bayes estimators. Simulation experiments are performed to see the effectiveness of the different estimators. Finally, a real dataset has been analyzed for illustrative purposes.

An Estimation of the Entropy for a Rayleigh Distribution Based on Doubly-Generalized Type-II Hybrid Censored Samples

In this paper, based on a doubly generalized Type II censored sample, the maximum likelihood estimators (MLEs), the approximate MLE and the Bayes estimator for the entropy of the Rayleigh distribution are derived. We compare the entropy estimators’ root mean squared error (RMSE), bias and Kullback–Leibler divergence values. The simulation procedure is repeated 10,000 times for the sample size n = 10, 20, 40 and 100 and various doubly generalized Type II hybrid censoring schemes. Finally, a real data set has been analyzed for illustrative purposes.

Statistical Selection Strategy for Risk and Protective Rare Variants Associated with Complex Traits

In genetic association studies with deep sequencing data, it is a challenging statistical problem to precisely locate rare variants associated with complex diseases or traits due to the limited number of observed genetic mutations. In particular, both risk and protective rare variants can be present in the same gene or genetic region. There currently exist very few statistical methods to separate casual rare variants from noncausal variants within a disease/trait-related gene or a genetic region, while there are relatively many statistical tests to detect a phenotypic association of a group of rare variants such as a gene or a genetic region. In this article, we propose a new statistical selection strategy that is able to locate causal rare variants within the disease/trait-related gene or a genetic region. The proposed procedure is to linearly combine potential risk and protective variants in order to find the optimal combination of rare variants that can have the strongest association signal. It is also computationally very efficient since the procedure is based on forward selection. In simulation studies we demonstrate that the selection performance of the proposed procedure is more powerful than other existing methods when both risk and protective variants are present. We also applied it to the real sequencing data on the ANGPTL gene family from the Dallas Heart Study.

Estimation of the Exponential Distributions based on Multiply Progressive Type II Censored Sample

The maximum likelihood(ML) estimation of the scale parameters of an exponential distribution based on progressive Type II censored samples is given. The sample is multiply censored (some middle observations being censored); however, the ML method does not admit explicit solutions. In this paper, we propose multiply progressive Type II censoring. This paper presents the statistical inference on the scale parameter for the exponential distribution when samples are multiply progressive Type II censoring. The scale parameter is estimated by approximate ML methods that use two different Taylor series expansion types (AMLEI, AMLEII). We also obtain the maximum likelihood estimator(MLE) of the scale parameter under the proposed multiply progressive Type II censored samples. We compare the estimators in the sense of the mean square error(MSE). The simulation procedure is repeated 10,000 times for the sample size n = 20 and 40 and various censored schemes. The AMLEII is better than MLE and AMLEI in the sense of the MSE.

Inference Based on Generalized Doubly Type-II Hybrid Censored Sample from a Half Logistic Distribution

Abstract Chandrasekar et al. (2004) introduced a generalized Type-II hybrid censoring. In this paper, we proposegeneralized doubly Type-II hybrid censoring. In addition, this paper presents the statistical inference on the scaleparameter ˙for the half logistic distribution when samples are generalized doubly Type-II hybrid censoring. Theapproximate maximum likelihood(AMLE) method is developed to estimate the unknown parameter. The scaleparameter ˙is estimated by the AMLE method using two di erent Taylor series expansion types. We comparethe AMLEs in the sense of the mean square error(MSE). The simulation procedure is repeated 10,000 times forthe sample size n = 20;30;40 and various censored samples. The AMLE I is better than AMLE II in the sense ofthe MSE.Keywords: Approximate maximum likelihood estimator, generalized doubly Type-II hybrid cen-sored sample, half logistic distribution. 1. Introduction Consider a life testing experiment in which nunits are put on test. Assume that the life times of nunitsare independent and identically distributed(i.i.d) as half logistic distribution with probability densityfunction(pdf)f

Bayesian and maximum likelihood estimations of the inverted exponentiated half logistic distribution under progressive Type II censoring

ABSTRACT In this paper, the estimation of parameters, reliability and hazard functions of a inverted exponentiated half logistic distribution (IEHLD) from progressive Type II censored data has been considered. The Bayes estimates for progressive Type II censored IEHLD under asymmetric and symmetric loss functions such as squared error, general entropy and linex loss function are provided. The Bayes estimates for progressive Type II censored IEHLD parameters, reliability and hazard functions are also obtained under the balanced loss functions. However, the Bayes estimates cannot be obtained explicitly, Lindley approximation method and importance sampling procedure are considered to obtain the Bayes estimates. Furthermore, the asymptotic normality of the maximum likelihood estimates is used to obtain the approximate confidence intervals. The highest posterior density credible intervals of the parameters based on importance sampling procedure are computed. Simulations are performed to see the performance of the proposed estimates. For illustrative purposes, two data sets have been analyzed.

SNP analysis of genes related to cholesterol metabolism and associated with late-onset Alzheimer’s disease

Late onset Alzheimer’s disease (LOAD) is the most common type of dementia and is characterized by impaired cholesterol homeostasis. Genome-wide association studies (GWAS) have shown that APOE, TOMM40, CLU, SORL1, PICALM, and BIN1 are related to cholesterol metabolism. To characterize the association between single-nucleotide polymorphisms (SNPs) and LOAD, we sequenced the SNP regions of the identified genes in a total of 11 LOAD cases and 12 healthy case controls in the Korean population. The SNP data showed a relatively high frequency in LOAD samples compared to the control samples. LOAD samples showed an average of 2.9 SNPs, whereas normal controls showed an average of 1.5 SNPs in the genes. Taken together, six genes associated with cholesterol metabolism using SNP analysis have shown frequent genetic variations in LOAD.

Goodness-of-Fit Test for the Normality based on the Generalized Lorenz Curve

Abstract Testingnormalityisveryimportantbecausethemostcommonassumptionisnormalityinstatisticalanalysis.We propose a new plot and test statistic to goodness-of-fit test for normality based on the generalized Lorenzcurve. We compare the new plot with the Q-Q plot. We also compare the new test statistic with the Kolmogorov-Smirnov (KS), Cramer-von Mises (CVM), Anderson-Darling (AD), Shapiro-Francia (SF), and Shapiro-Wilks( W ) test statistic in terms of the power of the test through by Monte Carlo method. As a result, new plot is clearlyclassified normality and non-normality than Q-Q plot; in addition, the new test statistic is more powerful than theother test statistics for asymmetrical distribution. We check the proposed test statistic and plot using Hodgkin’sdisease data.Keywords: Generalized Lorenz curve, goodness-of-fit, Lorenz curve, normality test, power. 1. Introduction Testing normality is very important because the most common assumption is normality in statisticalanalysis. Sonormalitywasresearchedcontinuouslybymanyscholars. Estimationofdatadistributionis used to histogram, Q-Q plot and P-P plot which uses a graph. In addition to using the graphicmethod, typical methods using the test statistic are the Kolmogorov-Smirnov test and Shapiro-Wilktest.ThisstudyproposesageneralizedLorenzcurve(GLC)teststatisticandagraphicalmethod,calledthe