Displaying similar documents to “On optimality of the LR tests in the sense of exact slopes. II. Application to individual distributions”

On two tests based on disjoint m-spacings

Franciszek Czekała (1998)

Applicationes Mathematicae

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This paper is concerned with the properties of two statistics based on the logarithms of disjoint m-spacings. The asymptotic normality is established in an elementary way and exact and asymptotic means and variances are computed in the case of uniform distribution on the interval [0,1]. This result is generalized to the case when the sample is drawn from a distribution with positive step density on [0,1]. Bahadur approximate efficiency of tests based on those statistics is found for...

Adaptive goodness-of-fit testing from indirect observations

Cristina Butucea, Catherine Matias, Christophe Pouet (2009)

Annales de l'I.H.P. Probabilités et statistiques

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In a convolution model, we observe random variables whose distribution is the convolution of some unknown density and some known noise density . We assume that is polynomially smooth. We provide goodness-of-fit testing procedures for the test : = , where the alternative is expressed with respect to 𝕃 2 -norm (i.e. has the form ψ n - 2 ∥ f - f 0 ∥ 2 2 ≥ 𝒞 ). Our procedure is adaptive with respect to the unknown smoothness parameter of . Different testing rates ( ...

Reliability for Beta Models

Nadarajah, Saralees (2002)

Serdica Mathematical Journal

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In the area of stress-strength models there has been a large amount of work as regards estimation of the reliability R = Pr(X2 < X1 ) when X1 and X2 are independent random variables belonging to the same univariate family of distributions. The algebraic form for R = Pr(X2 < X1 ) has been worked out for the majority of the well-known distributions including Normal, uniform, exponential, gamma, weibull and pareto. However, there are still many other distributions for which the form...