Testing Equality of Coefficients of Variation of Two Populations

The test statistics are proposed for testing the equality of the coefficients of variation of two normal populations based on independent samples. The asymptotic distributions of the statistics are approximated by well-known distributions. The empirical sizes and powers of these statistics are computed and compared.     

Some Distributions of Induced Records

In this paper we discuss the properties of concomitants of record values. The distributions of the concomitants in the sequence of record values of bivariate distributions are obtained and their possible applications in the areas of biosciences have been pointed out.     

Estimation of a Conditional Mean in a Linear Regression Model

Consider the two linear regression models of Y_ij on X_ij, namely Y_ij = β_io + β_il X_ij + ε_ij,j = 1,2,…,n_i, i = 1,2, where ε_ij are assumed to be normally distributed with zero mean and common unknown variance σ². The estimated value of a mean of Y₁ for a given value of X₁ is made to depend on a preliminary test of significance of the hypothesis β₁₁ = β₂₁. The bias and the mean square error of the estimator for the conditional mean of Y₁ are given. The relative efficiency of the estimator to the usual estimator is computed and is used to determine a proper choice of the significance level of the preliminary test.     

On a Characterization of the Exponential Distribution by Weak Homoscedasticity of Record Values

A sequence {X_n, n≤1} of independent and identically distributed random values with continuous cumulative distribution function F(x) is considered. X_j is a record value of this sequence if X_j ≤ max (X₁, X₂, …, X_j?1). We define L(n)=min.(j!j>L(n?1.), X_j<X_L(n?1)), with L(0) = 1. Let Z_n=X_L(n)? X_L(n?1), n ≤ 1. We will show that the conditional variance of Z_n given X_L(n?1)=x does not depend on × if and only if F(x) is exponential.     

A Monte Carlo Study of Robustness of Pretest and Shrinkage Estimators in Pooling Coefficients of Variation

Pooling data, when justified, is advantageous for estimating the true parameter. In this paper the problem of estimating the coefficient of variation is considered when it is a priori suspected that two coefficients of variation are the same. Various estimators based on pretest and shrinkage rules are considered. A comparison through the Simulated Mean Squared Error (SMSE) criterion is carried out among various proposed estimators of the target coefficient of variation. The relative simulated efficiencies of the restricted, shrinkage restricted and shrinkage pretest estimators are studied. It is found that the proposed estimators are quite robust when the sample sizes are not too large. The result of Monte Carlo study indicates that the proposed shrinkage pretest estimator is efficient than the usual estimator in a wider range.     

Two Characteristic Properties of the Generalized Negative Binomial Distribution

Infinite divisibility condition and a relation between the mean and variance are used to characterize the generalized negative binomial distribution.     

A Note on the Characterization of the Normal Distribution

Suppose X₁, X₂,…, X_n are independent and identically distributed random variables with absolutely continuous distribution function F. It is known that if F is standard normal distribution then (i)∑X²_i is a chi-square with n degrees of freedom and (ii)nX¯² is a chi-square with 1 degrees of freedom where X¯=1/n ∑X_i. Here the above two properties are utilized to characterize the normal distribution.     

Testis-specific fascin component FSCN3 is dispensable for mouse spermatogenesis and fertility

Molecular Biology Reports - Fascins belong to a family of actin-bundling proteins that are involved in a wide range of biological functions. FSCN3, a newly identified testis-specific actin-bundling...     

Estimation of a Conditional Mean in a Linear Regression Model after a Preliminary Test on Regression Coefficient

Consider the two linear regression models of Y_ij on X_ij, namely Y_ij = β_io + β_ij, X_ij + E_ij = 1, 2,…, n_i, i = 1, 2, where E_ij are assumed to be normally distributed with zero mean and common unknown variance σ². The problem of estimating the conditional mean of Y₁ for a given value of X₁ is considered when it is a priori suspected that β₁₀ = β₂₀ and β₁₁ = β₂₁. The preliminary test estimator is proposed. The exact expressions for the bias and the mean square error of the estimator are derived. The relative efficiency of the new estimator to the usual least square estimator based on the first regression alone is computed and is used to determine the appropriate value of the significance level of the preliminary test β₁₀ = β₂₀ and β₁₁ = β₂₁.