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In ultraviolet communications, the transceiver jitter effects have been ignored in previous studies, something that can result in non-negligible performance degradation especially in vibration states or in mobile scenes. To address this issue, we model the relationship between the received power and transceiver jitter by making use of a moment-based density function approximation method. Based on this relationship, we incorporate the transceiver jitter effects in combination with the Poisson distribution. The error rate results are obtained assuming on–off key modulation with optimal threshold-based detection. We validate the error rate expressions by comparing the analytical results to Monte Carlo simulation results. The results show that the transceiver jitter effects cause performance degradation especially in smaller transceiver elevation angles or shorter range cases, which are often adopted in short-range ultraviolet communications. The results also show that larger elevation angle cases have a better performance with respect to antijitter and may perform better compared to smaller elevation angle situations in the case of a larger standard deviation of jitter. This work studies for the first time the transceiver jitter effects in ultraviolet communications and provides guidelines for experimental system design.

Stein-type shrinkage techniques are applied to the parametric components of a semi-nonparametric regression model recently proposed by (Ma et al. 2015: 285–303). On the basis of an uncertain prior information (restrictions) about the parameters of interest, shrinkage techniques are shown to improve the accuracy of the model. The effectiveness of the proposed estimators are corroborated by a simulation study.

This paper proposes a moment-based approximation to the distribution of quadratic forms in gamma random variables. Quadratic forms in order statistics from an exponential population are considered as well. Actually, several test statistics can be expressed in terms of the latter. The density approximants are expressible as the product of a gamma type distributed base density function and a polynomial adjustment. Several illustrative examples are provided.

In this paper, we focus our attention on a novel Bayesian approach to determine mRNA levels from quality control indicators (QCI), such as Background, Percent Present, Scale Factor GAPDH and ß-Actin. QCI data can be modelled as symmetrical and asymmetrical probability distributions. We discuss the identification of statistical probability models from QCI sample data sets as well as the derivation of mRNA predictive distributions by making use of a novel Bayesian approach in this context.

SYNOPTIC ABSTRACTA recursive relationship for determining the moments of a quadratic form in normal variables as well as an explicit formula for approximating a continuous density function defined on a compact support from its moments are derived in this paper. Each of these results have, on their own, a plethora of applications as quadratic forms are ubiquitous in Statistics and the moments of most test statistics that are confined to closed intervals can be readily evaluated; they are combined herewith to produce an approximation to the null distribution of the Durbin-Watson statistic, which for all intents and purposes, can be viewed as exact. The proposed approach takes into account the observation matrix of explanatory variables associated with the assumed regression model, and more accuracy can always be gained by making use of additional moments. Furthermore, the Durbin-Watson statistic is shown to be invariant in the class of spherically distributed error vectors, and an integral formula is derived for evaluating its moments under the assumption that the error vector has a general covariance structure. A numerical example illustrates the proposed methodology.

This article derives the likelihood ratio statistic to test the independence between (X1,…,Xr) and (Xr+1,…,Xk) under the assumption that (X1,…,Xk) has a multivariate normal distribution and that a sample of size n is available, where for N observation vectors all components are available, while for M = (n + N) observation vectors, the data on the last q components, (Xk-q+1,…,Xk) are missing (k+q≥r).

The exact distribution function of the ratio of two sums of gamma variates is derived in this paper. The result applies to ratios of quadratic forms and to a statistic used for testing the equality of scale parameters in two gamma populations.

This paper provides computable representations for the evaluation of the probability content of cones in isotropic random fields. A decomposition of quadratic forms in spherically symmetric random vectors is obtained and a representation of their moments is derived in terms of finite sums. These results are combined to obtain the distribution function of quadratic forms in spherically symmetric or central elliptically contoured random vectors. Some numerical examples involving the sample serial covariance are provided. Ratios of quadratic forms are also discussed.

The exact density of the difference of two linear combinations of independent noncentral chi-square variables is obtained in terms of Whittaker's function and expressed in closed forms. Two distinct representations are required in order to cover all the possible cases. The corresponding expressions for the exact distribution function are also given.

A computable expression is derived for the raw moments of the random variableZ=N/D whereN=S1nmiXi+Sn+1smiXi,D=Sn+1sliXi+Ss+1rniXi, and theXi's are independently distributed central chi-square variables. The first four moments are required for approximating the distribution ofZ by means of Pearson curves. The exact density function ofZ is obtained in terms of sums of generalized hypergeometric functions by taking the inverse Mellin transform of theh-th moment of the ratioN/D whereh is a complex number. The casen=1,s=2 andr=3 is discussed in detail and a general technique which applies to any ratio having the structure ofZ is also described. A theoretical example shows that the inverse Mellin transform technique yields the exact density function of a ratio whose density can be obtained by means of the transformation of variables technique. In the second example, the exact density function of a ratio of dependent quardratic forms is evaluated at various points and then compared with simulated values.

An alternate representation of the densities of some test statistics for the structural coefficients of the multivariate linear functional relationship model is proposed in this article. These statistics are distributed as the ratio of a linear combination of chi-square variÂtes over the root of a product of chi-square variÂtes. A computable representation of their densities has already been derived by Provost (1984) with the help of the technique of the inverse Mellin transform. The connection of the alternate representation to the densities of products of independent beta type-2 and of independent F-random variables is also discussed.