In this paper we estimate R = P{X ≤ Y } when X and Y are independent random variables from geometric and Poisson distribution respectively. We find maximum likelihood estimator of R and its asymptotic distribution. This asymptotic distribution is used to construct asymptotic confidence intervals. A procedure for deriving bootstrap confidence intervals is presented. UMVUE of R and UMVUE of its v...

The problem of fixed-width Confidence Interval for the mean survival time is considered. Sequential procedures are adopted based on the maximum likelihood estimators (MLE) and uniform minimum variance unbiased estimators (UMVUE) of the scale parameter. A comparative study of the two sequential procedures is done and second-order approximations are obtained and they are proved to be ‘asymptotica...

Let X1,X2, . . . ,Xn be a random sample from a normal N(θ,σ2) distribution with an unknown mean θ = 0,±1,±2, . . . . Hammersley (1950) proposed the maximum likelihood estimator (MLE) d = [Xn], nearest integer to the sample mean, as an unbiased estimator of θ and extended the Cramér-Rao inequality. The Hammersley lower bound for the variance of any unbiased estimator of θ is significantly improv...

This paper presents an important theorem, which shows that, heading from the moments of standard normal distribution, one can generate density functions originating a family models. Additionally, we discussed that different random variable domains are achieved with transformations. For instance, adopted moment order two, proposed and transformed it, enabled us to exemplify this class as unit di...

An estimator is said to be unbiased if b(θ̂) = 0. If multiple unbiased estimates of θ are available, and the estimators can be averaged to reduce the variance, leading to the true parameter θ as more observations are available. Placing the unbiased restriction on the estimator simplifies the MSE minimization to depend only on its variance. The resulting estimator, called the Minimum Variance Unb...

In this article, we consider the estimation of P[Y < X], when strength, X and stress, Y are two independent variables of Burr Type XII distribution. The MLE of the R based on one simple iterative procedure is obtained. Assuming that the common parameter is known, the maximum likelihood estimator, uniformly minimum variance unbiased estimator and Bayes estimator of P[Y < X] are discussed. The ex...

It has been shown that the uniformly minimum variance unbiased (UMVU) estimator of the generalized variance always exists for any natural exponential family. In practice, however, this estimator is often di¢ cult to obtain. This paper explicitly identi…es the results in complete bivariate and symmetric multivariate gamma models, which are diagonal quadratic exponential families. For the non-ind...

Abstract The exponentiated Burr Type XII (EBXII) distribution has wide applications in reliability and economic studies. In this article, the estimation of probability density function cumulative EBXII is considered. We examine maximum likelihood estimator, uniformly minimum variance unbiased least squares weighted product spacing Cramér–von-Mises Anderson–Darling estimator. derive analytical f...