The stochastic solution to a diffusion equations with polynomial coefficients is called a Pearson diffusion. If the first time derivative is replaced by a Caputo fractional derivative of order less than one, the stochastic solution is called a fractional Pearson diffusion. This paper develops an explicit formula for the covariance function of a fractional Pearson diffusion in steady state, in t...

Motivated by problems of anomaly detection, this paper implements the Neyman-Pearson paradigm to deal with asymmetric errors in binary classification with a convex loss. Given a finite collection of classifiers, we combine them and obtain a new classifier that satisfies simultaneously the two following properties with high probability: (i), its probability of type I error is below a pre-specifi...

Motivated by problems of anomaly detection, this paper implements the Neyman-Pearson paradigm to deal with asymmetric errors in binary classification with a convex loss. Given a finite collection of classifiers, we combine them and obtain a new classifier that satisfies simultaneously the two following properties with high probability: (i) its probability of type I error is below a pre-specifie...

For the measurement of Ns signals in N events rigorous confidence bounds on the true signal probability pexact were established in a classical paper by Clopper and Pearson [Biometrica 26, 404 (1934)]. Here, their bounds are generalized to the HEP situation where cuts on the data tag signals with probability Ps and background data with likelihood Pb < Ps. The Fortran program which, on input of P...

The Chi-Square test (χ 2 test) is a family of tests based on a series of assumptions and is frequently used in the statistical analysis of experimental data. The aim of our paper was to present solutions to common problems when applying the Chi-square tests for testing goodness-of-fit, homogeneity and independence. The main characteristics of these three tests are presented along with various p...

Karl Pearson was a man of many parts: the applied mathematician who completed Todhunter's History of the Theory of Elasticity; the philosopher of science whom Lenin described as 'this conscientious and honest opponent of materialism' (1970, p. 170); the statistician who espoused the cause of evolution and edited Biometrika for 35 years; the innovator and administrator whose Department became fa...

Little guidance is available concerning the type of children's ward accommodation most suitable for the tropics. Hospitals are still being built without any children's wards and special facilities for neonates are seldom found outside teaching hospitals. Where such facilities exist, design has conformed to the traditional type of premature baby unit, which may be neither suitable nor desirable ...