# Statistics & Probability Letters

Statistics and Probability Letters > 1995 > 22 > 1 > 1-6

Statistics and Probability Letters > 1995 > 22 > 1 > 71-77

_{t}:t = 0, 1, } be a discrete-parameter irreducible semi-Markov process with a finite partitioned state space S = A

_{1}A

_{2}. In this paper, a closed form expression is derived for the cumulative distribution function of the number of visits by Y to A

_{1}during the first t + 1 time instants for which hitherto results in the Laplace transform domain only had...

Statistics and Probability Letters > 1995 > 22 > 1 > 17-23

Statistics and Probability Letters > 1995 > 22 > 1 > 33-42

Statistics and Probability Letters > 1995 > 22 > 1 > 43-47

Statistics and Probability Letters > 1995 > 22 > 1 > 79-85

Statistics and Probability Letters > 1995 > 22 > 1 > 25-31

^{d}, and being once differentiable. As an application we show that the maximum of the Brownian sheet on a rectangle [0, s] [0, t] possesses an infinitely differentiable density.

Statistics and Probability Letters > 1995 > 22 > 1 > 7-15

Statistics and Probability Letters > 1995 > 22 > 1 > 59-69

Statistics and Probability Letters > 1995 > 22 > 1 > 55-57

Statistics and Probability Letters > 1995 > 22 > 1 > 49-53

Statistics and Probability Letters > 1995 > 22 > 2 > 149-156

_{i}} of standard Gaussian random variables, the strong uniform consistency of the kernel density estimates for sequence {Y

_{i}} modeled byY

_{i}= H(X

_{t}

_{1}

^{+}

^{1}

^{i}, , X

_{t}

_{d}

^{+}

^{i}) is proved.

Statistics and Probability Letters > 1995 > 22 > 2 > 167-173

_{1}, X

_{2}) be a bivariate random variable of the discrete type with joint probability density functionp

_{i}

_{j}= pr[X

_{1}= i,X

_{2}= j], i, j = 1, ,k. Based on a random sample from this distribution, we discuss the properties of the likelihood ratio test of the null hypothesis of bivariate symmetry H

_{0}: p

_{i}

_{j}= p

_{j}

_{i}(i,...

Statistics and Probability Letters > 1995 > 22 > 2 > 157-160

^{2}test for the symmetry...

Statistics and Probability Letters > 1995 > 22 > 2 > 111-119

Statistics and Probability Letters > 1995 > 22 > 2 > 87-96

_{n}(X

_{n})}, the functional of a countable nonhomogeneous Markov chain {X

_{n}}. A class of strong laws of large numbers for these processes, which are different from the usual ones, are obtained. In the theorems of this paper, the expectationE (f

_{n}(X

_{n})) in the usual strong laws...

Statistics and Probability Letters > 1995 > 22 > 2 > 97-102

Statistics and Probability Letters > 1995 > 22 > 2 > 103-110

Statistics and Probability Letters > 1995 > 22 > 2 > 131-136

Statistics and Probability Letters > 1995 > 22 > 2 > 121-129