Displaying similar documents to “From the general affine transform family to a Pareto type IV model.”

Inference on overlap coefficients under the Weibull distribution : equal shape parameter

Obaid Al-Saidy, Hani M. Samawi, Mohammad F. Al-Saleh (2005)

ESAIM: Probability and Statistics

Similarity:

In this paper we consider three measures of overlap, namely Matusia’s measure ρ , Morisita’s measure λ and Weitzman’s measure Δ . These measures are usually used in quantitative ecology and stress-strength models of reliability analysis. Herein we consider two Weibull distributions having the same shape parameter and different scale parameters. This distribution is known to be the most flexible life distribution model with two parameters. Monte Carlo evaluations are used to study the bias...

Large deviations for independent random variables – Application to Erdös-Renyi’s functional law of large numbers

Jamal Najim (2005)

ESAIM: Probability and Statistics

Similarity:

A Large Deviation Principle (LDP) is proved for the family 1 n ∑ 1 n 𝐟 ( x i n ) · Z i n where the deterministic probability measure 1 n ∑ 1 n δ x i n converges weakly to a probability measure R and ( Z i n ) i ∈ ℕ are ℝ d -valued independent random variables whose distribution depends on x i n and satisfies the following exponential moments condition: sup i , n 𝔼 e α * | Z i n | < + ∞ forsome 0 < α * < + ∞ . In this context, the identification of the rate function is non-trivial due to the absence of equidistribution. We rely on fine convex analysis to address this issue. Among...

Probabilities of discrepancy between minima of cross-validation, Vapnik bounds and true risks

Przemysław Klęsk (2010)

International Journal of Applied Mathematics and Computer Science

Similarity:

Two known approaches to complexity selection are taken under consideration: n-fold cross-validation and structural risk minimization. Obviously, in either approach, a discrepancy between the indicated optimal complexity (indicated as the minimum of a generalization error estimate or a bound) and the genuine minimum of unknown true risks is possible. In the paper, this problem is posed in a novel quantitative way. We state and prove theorems demonstrating how one can calculate pessimistic...