Extreme value analysis for emerging African markets

For the first time, an extreme value analysis is provided for financial data from Africa. The results of analysis show evidence of emerging economies in Africa.     

An investigation of effective factors on children’s growth failure in Iran using multilevel models

Quality & Quantity - Delay or stop in children’s growth is referred to as failure to thrive (abbreviated as FTT) which leads to adverse effects such as increased mortality, reduced...     

Pearson type VII ratio distribution

In modern decision-making processes, ratios or indices of stochastic variables are commonly used criteria. The decision criterion is, however, frequently presented as deterministic despite the fact that sampling has been the dominant collection method for the data underlying the measure. This paper derives the exact distribution of |X/Y| when X and Y are independent Pearson type VII random variables. We provide an application of this result to the exchange rate data of the six major currencies. Some computer programs for use in the applications are also provided.      

Almost sure central limit theorem for the products of <Emphasis Type="Italic">U</Emphasis>-statistics

Let (X _n ) be a sequence of i.i.d random variables and U _n a U-statistic corresponding to a symmetric kernel function h, where h ₁(x ₁) = Eh(x ₁, X ₂, X ₃, . . . , X _m ), μ = E(h(X ₁, X ₂, . . . , X _m )) and ? ₁ = Var(h ₁(X ₁)). Denote \({\gamma=\sqrt{\varsigma_{1}}/\mu}\), the coefficient of variation. Assume that P(h(X ₁, X ₂, . . . , X _m ) > 0) = 1, ? ₁ > 0 and E|h(X ₁, X ₂, . . . , X _m )|³ < ∞. We give herein the conditions under which

$\lim_{N\rightarrow\infty}\frac{1}{\log N}\sum_{n=1}^{N}\frac{1}{n}g\left(\left(\prod_{k=m}^{n}\frac{U_{k}}{\mu}\right)^{\frac{1}{m\gamma\sqrt{n}}}\right) =\int\limits_{-\infty}^{\infty}g(x)dF(x)\quad {\rm a.s.}$

for a certain family of unbounded measurable functions g, where F(·) is the distribution function of the random variable \({\exp(\sqrt{2} \xi)}\) and ξ is a standard normal random variable.

     

On the Ratio of Fréchet Random Variables

The distribution of the ratio X/Y is derived when X and Y are independent Fréchet random variables. Extensive tabulations of the associated percentage points are also given.     

Probability Integrals of the Multivariate t Distribution

Results on probability integrals of multivariate t distributions are reviewed. The results discussed include: Dunnett and Sobel's probability integrals, Gupta and Sobel's probability integrals, John's probability integrals, Amos and Bulgren's probability integrals, Steffens' non‐central probabilities, Dutt's probability integrals, Amos' probability integral, Fujikoshi's probability integrals, probabilities of cone, probabilities of convex polyhedra, probabilities of linear inequalities, maximum probability content, and Monte Carlo evaluation.     

The misclassification error of the maximum likelihood procedure when deciding among a finite choice of distributions

Suppose we have a sample randomly drawn from one of a given number of distributions. We wish to select the distribution based on the optimal maximum likelihood procedure. In this note, various tight estimates are derived under general conditions for the probability of making the wrong selection. The estimates are also extended to the case of many exponential families, where the general conditions fail. Some of the estimates are illustrated by means of simulation. The practical use of the estimates is discussed.     

On a distribution of Jasso and Kotz

Explicit expressions are derived for the moments and the Gini coefficient of the ring-exponential distribution introduced by Jasso and Kotz ( Statistica Neerlandica , 61 , 2007, 305–328).