On the quadratic derivative of exponential probabilities
In the paper it is shown that exponential families of probabilities have the quadratic derivative of the likelihood ratio, and explicit formulas for this derivative are derived.
On the ratio of gamma and Rayleigh random variables
The gamma and Rayleigh distributions are two of the most applied distributions in engineering. Motivated by engineering issues, the exact distribution of the quotient X/Y is derived when X and Y are independent gamma and Rayleigh random variables. Tabulations of the associated percentage points and a computer program for generating them are also given.
On the ratio of Pearson type VII and Bessel random variables.
On The Resolution Of A Mixture Of Observations From Two Modified Power Series Distributions.
On the restricted range in the samples from the gamma population
Samples from the gamma population are considered which are censored both above and below, that is, observations below and observations above are missing among observations. The range in such censored samples is taken up and the distribution of this restricted range is obtained, which can be compared with that in the complete sample case given in a previous paper.
On the robustness of properties characterizing the normal distribution
On the significance level of the multirelation coefficient.
On the spectrum of a distribution function and on unique factorization.
On the two-sided quality control
Let the random variable have the normal distribution . Explicit formulas for maximum likelihood estimator of are derived under the hypotheses , where are arbitrary fixed numbers. Asymptotic distribution of the likelihood ratio statistic for testing this hypothesis is derived and some of its quantiles are presented.
On the use of difference of two proportions
Differences of two proportions occur most frequently in biomedical research. However, as far as published work is concerned, only approximations have been used to study the distribution of such differences. In this note, we derive the exact probability distribution of the difference of two proportions for seven flexible beta type distributions. The expressions involve several well known special functions. The use of these results with respect to known approximations is illustrated.
On Three and Five Parameter Bivariate Beta Distributions.
On two fragmentation schemes with algebraic splitting probability
Consider the following inhomogeneous fragmentation model: suppose an initial particle with mass x₀ ∈ (0,1) undergoes splitting into b > 1 fragments of random sizes with some size-dependent probability p(x₀). With probability 1-p(x₀), this particle is left unchanged forever. Iterate the splitting procedure on each sub-fragment if any, independently. Two cases are considered: the stable and unstable case with and respectively, for some a > 0. In the first (resp. second) case, since smaller...
On two theorems of Bartoszewicz
On uniform tail expansions of bivariate copulas
The theory of copulas provides a useful tool for modelling dependence in risk management. The goal of this paper is to describe the tail behaviour of bivariate copulas and its role in modelling extreme events. We say that a bivariate copula has a uniform lower tail expansion if near the origin it can be approximated by a homogeneous function L(u,v) of degree 1; and it is said to have a uniform upper tail expansion if the associated survival copula has a lower tail expansion. In this paper we (1)...
On useful schema in survival analysis after heart attack
Recent model of lifetime after a heart attack involves some integer coefficients. Our goal is to get these coefficients in simple way and transparent form. To this aim we construct a schema according to a rule which combines the ideas used in the Pascal triangle and the generalized Fibonacci and Lucas numbers
On weak convergence of sequences of measures
Operator semigroups and Poisson convergence in selected metrics.
Optimal mean-variance bounds on order statistics from families determined by star ordering
We present optimal upper bounds for expectations of order statistics from i.i.d. samples with a common distribution function belonging to the restricted family of probability measures that either precede or follow a given one in the star ordering. The bounds for families with monotone failure density and rate on the average are specified. The results are obtained by projecting functions onto convex cones of Hilbert spaces.
Optimization of the size of nonsensitiveness regions
The problem is to determine the optimum size of nonsensitiveness regions for the level of statistical tests. This is closely connected with the problem of the distribution of quadratic forms.