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Alternative Tools of Statistical Analysis: L-moments and TL-moments of Probability Distributions
Issue:
Volume 3, Issue 2, April 2014
Pages:
14-25
Received:
22 March 2014
Accepted:
10 April 2014
Published:
20 April 2014
Abstract: Moments and cumulants are commonly used to characterize the probability distribution or observed data set. The use of the moment method of parameter estimation is also common in the construction of an appropriate parametric distribution for a certain data set. The moment method does not always produce satisfactory results. It is difficult to determine exactly what information concerning the shape of the distribution is expressed by its moments of the third and higher order. In the case of small samples in particular, numerical values of sample moments can be very different from the corresponding values of theoretical moments of the relevant probability distribution from which the random sample comes. Parameter estimations of the probability distribution made by the moment method are often considerably less accurate than those obtained using other methods, particularly in the case of small samples. The present paper deals with an alternative approach to the construction of an appropriate parametric distribution for the considered data set using order statistics
Abstract: Moments and cumulants are commonly used to characterize the probability distribution or observed data set. The use of the moment method of parameter estimation is also common in the construction of an appropriate parametric distribution for a certain data set. The moment method does not always produce satisfactory results. It is difficult to determ...
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On the System Analysis of the Foundations of Trigonometry
Issue:
Volume 3, Issue 2, April 2014
Pages:
26-39
Received:
28 March 2014
Accepted:
18 April 2014
Published:
30 April 2014
Abstract: Analysis of the foundations of standard trigonometry is proposed. The unity of formal logic and of rational dialectics is methodological basis of the analysis. It is shown that the foundations of trigonometry contradict to the principles of system approach and contain formal-logical errors. The principal logical error is that the definitions of trigonometric functions represent quantitative relationships between the different qualities: between qualitative determinacy of angle and qualitative determinacy of rectilinear segments (legs) in rectangular triangle. These relationships do not satisfy the standard definition of mathematical function because there are no mathematical operations that should be carry out on qualitative determinacy of angle to obtain qualitative determinacy of legs. Therefore, the left-hand and right-hand sides of the standard mathematical definitions have no the identical sense. The logical errors determine the essence of trigonometry: standard trigonometry is a false theory.
Abstract: Analysis of the foundations of standard trigonometry is proposed. The unity of formal logic and of rational dialectics is methodological basis of the analysis. It is shown that the foundations of trigonometry contradict to the principles of system approach and contain formal-logical errors. The principal logical error is that the definitions of tri...
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A Convex Hull’ Characterization
Franco Fineschi,
Giovanni Quaranta
Issue:
Volume 3, Issue 2, April 2014
Pages:
40-48
Received:
11 April 2014
Accepted:
7 May 2014
Published:
20 May 2014
Abstract: Conditions so that a vector belongs to a convex hull are obtained. Multilinear convex functions are considered. If these maps are defined on a convex set, it is obtained the algebraic expression. As an application, infinite games, with linear convex payoff, are studied.
