On Kendall's Autocorrelations

This brief article extends the theory of sample Kendall's autocorrelations by providing their exact variances at lags higher than one under the null hypothesis of randomness, by introducing and investigating their weighted modifications, and by numerical demonstration of these results and their usefulness.     

An Investigation of Agreement Between the Item Difficulty Coefficient Calculated in Accordance With Classical Test Theory and Item Response Theory With Bland–Altman Method

The purpose of this study is to investigate agreement between item difficulty coefficients calculated relying on classical test theory and item response theory with Bland–Altman method. According to results, although there is a high correlation between Pj and b coefficient estimated with HGLM (hierarchical generalized linear model), 1P, and 3P models, it can be said that there is no agreement between two methods and cannot be used interchangeably. It is observed that the confidence limit is wide according to Bland–Altman graphics. Therefore, it can be said that there is no agreement between item difficulty values obtained from two methods. Bland–Altman method which is used in clinical studies mostly is suggested to be used in the comparison of methods used especially in the evaluation of student performance in education, in agreement studies among specialist considerations especially in terms of providing additional information to the studies in which correlation coefficient is calculated.     

A cold standby repairable system with the repairman having multiple vacations and operational,repair, and vacation times following phase-type distributions

ABSTRACT

This paper studies a cold standby repairable system with two identical components and one repairman having multiple vacations applying matrix-analytic methods. The lifetime of the component follows a phase-type distribution. The repair times and the vacation times of the repairman are governed by different phase-type distributions, respectively. For this system, the Markov process governing the system is constructed. The system is studied in a transient and stationary regime, the availability, the reliability, the rates of occurrence of the different types of failures, and the working probability of the repairman are calculated, respectively. A numerical application is performed to illustrate the calculations.     

Identifiability of distributions under competing risks and complementary risks model

Let X₁,X₂,…,X_p be p random variables with cdf's F₁(x),F₂(x),…,F_p(x)respectively. Let U = min(X₁,X₂,…,X_p) and V = max(X₁,X₂,…,X_p).In this paper we study the problem of uniquely determining and estimating the marginal distributions F₁,F₂,…,F_p given the distribution of U or of V.

First the problem of competing and complementary risks are introduced with examples and the corresponding identification problems are considered when the X₁'s are independently distributed and U(V) is identified, as well as the case when U(V) is not identified. The case when the X₁'s are dependent is considered next. Finally the problem of estimation is considered.     

Estimation of pr{y<x) for truncation parameter distributions

Blackwell-Rao-Lehmann-Scheffe theory is used to derive the minimum variance ur biased estimator of P=Pr{Y<X} when the independent random variables X and Y follow thf truncation parameter distributions The two-parameter exponential, Pareto, power function and uniform distributions are considered in examples.     

Maximum likelihood estimation,from doubly censored samples,of the mean of a normal distribution with known coeffucient of variation

Let x be a random variable having the normal distribution with mean μ and variance c²μ², where c is a known constant. The maximum likelihood estimation of μ when the lowest r₁ and the highest r₂ sample values censored have been given the asymptotic variance of the maximum likelihood estimator is obtained.     

On some tests for independence in nonnormal situations: neyman'S C(A)test

A study is made of Neyman's C(a) test for testing independence in nonnormal situations. It is shown that it performs very well both in terms of the level of significance and the powereven for smallvalues of the samplesize. Also, in the case of the bivariate Polsson distribution, itis shown that Fisher's z and Student's t transforms of the sample correlation coefficient are good competitors for Neyman's procedure.