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The multisample version of the Lepage test

František Rublík (2005)

Kybernetika

The two-sample Lepage test, devised for testing equality of the location and scale parameters against the alternative that at least for one of the parameters the equality does not hold, is extended to the general case of k > 1 sampled populations. It is shown that its limiting distribution is the chi-square distribution with 2 ( k - 1 ) degrees of freedom. This k -sample statistic is shown to yield consistent test and a formula for its noncentrality parameter under Pitman alternatives is derived. For some particular...

The notion of randomness from Aristotle to Poincaré

O. B. Sheynin (1991)

Mathématiques et Sciences Humaines

Aristotle and even earlier scientist and philosophers attempted to define, or at least to through light upon randomness. The author sketches the attempts to direct concept of randomness into the realm of mathematical science from Aristotle up to Poincaré. He dwells on the various interpretations of randomness that were pronounced in natural science and philosophy, and on the interrelation between necessity and randomness.

The optimal control chart procedure

Jaroslav Skřivánek (2004)

Kybernetika

The moving average (MA) chart, the exponentially weighted moving average (EWMA) chart and the cumulative sum (CUSUM) chart are the most popular schemes for detecting shifts in a relevant process parameter. Any control chart system of span k is specified by a partition of the space k into three disjoint parts. We call this partition as the control chart frame of span k . A shift in the process parameter is signalled at time t by having the vector of the last k sample characteristics fall out of the...

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