UNBIASED ESTIMATION OF PARAMETRIC FUNCTIONS IN SAMPLING FROM TWO ONE-TRUNCATION PARAMETER FAMILIES

We consider the problem of minimum variance unbiased estimation of a U-estimable function of two unknown truncation parameters based on independent random samples from two one-truncation parameter families. In particular, we obtain the UMVU estimator of the probability that Y > X.     

Unbiased estimation in type II censored samples from a one-truncation parameter density

We consider uniform minimum variance unbiased estimation of a U-estimable function when the sample is (singly) Type II censored and comes from a one-truncation parameter density f(x;θ) = h(x) q(θ). An explicit expression for the estimator is derived. Shortest length confidence interval for q(θ) is obtained.     

Estimation of parameters under a random censorship model

The problem of estimation of parameters of a lifetime distribution is considered under the proportional hazards model of random censorship. Asymptotic variances of several estimators of survival function are compared in the eponential case.     

On the estimation of restricted mean

In sampling from a continuous distribution with unknown mean μ and variance σ² the problem of estimation of μ, when it is known that μ∈(a, ∞) (or μ∈(-∞, b)), is considered. The estimators proposed here lie in the interval (a, ∞) (or (-∞, b)) almost surely. The performance of these estimators is compared to that of some known estimators in the case of sampling from a normal, exponential and a weighted difference of two independent chi-square distributions.     

A class of distributions connected to order statistics with nonintegral sample size

Newton's binomial series expansion is used to develop a (class of) distribution function(s) F_r:∝ which may be interpreted as the distribution of the r^thorder statistic with nonintegral sample size∝. It is shown that F_r:∝ has properties similar to F_r:n. Multivariate extension is considered and an elementary proof of the integral representation for the joint distribution of a subset of order statistics is given. An application is included.     

Moments of order statistics from one truncation parameter densities

Analogs of some classical recurrence relations for moments of order statistics for a one truncation parameter densities are derived. These relate the k^thorder moment of the r^thorder statistic X_r:nto the k^thorder moment of X_l:ior X_r:rvia an integral operator. Similar results are obtained for product moments. An application is also given.     

Distribution of order statistics with random sample size

The distribution function of the ith order statistic in random sampling from a distribution function F is obtained when the sample size. is random.     

Estimation of parameters of location-scale family of distributions in complete and type ii censored samples

In this paper we consider the estimation of location, scale and quantile-function of a location-scale family of distributions in complete and Type II multicensored samples. Our method integrates the two well-known approaches to probability plotting, namely, the analytic method of Blom (1958) and the hazard plotting method due to Nelson (1972). Some important special cases of location-scale family of distributions are considered for details.     

Unbiased estimation of the common mean of a multivariate normal distribution

The problem of unbiased estimation of the common mean of a multivariate normal population is considered. An unbiased estimator is proposed which has a smaller variance than the usual estimator over a large part of the parameter space.     

Amplifying youth voices in the developing world

Low-literacy youth in the slums of Brazil have been historically unequipped to share their ideas on how to improve their lives, because outside of the spoken word, it is difficult for them to express their thoughts persuasively. The Amplifying Voices afterschool video program piloted at Projeto Uerê in Rio de Janeiro shows that youth can leverage technological tools to voice their perspectives on social issues relevant to themselves and their communities.