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Several coefficients, called divergences, have been suggested in the statistical literature to reflect the fact that some probability distributions are “closer together” than others and consequently that it may be easier to distinguish between the distributions of one pair than between those of another. When comparing three biological populations, it is often interesting to measure how two of them “move apart” from the third. Deals with the statistical analysis of this problem by means of bivariate divergence statistics. Provides a unified study, depicting the behaviour and relative merits of traditional divergences, by using the (h,ø), divergence family of statistics introduced by Menéndez et al.

Read (1984) presented an asymptotic expansion for the distribution function of the power divergence statistics whose speed of convergence is dependent on the parameter of the family. Generalizes that result by considering the family of (h, φ)‐divergence measures. Considers two other closer approximations to the exact distribution. Compares these three approximations for the Renyi’s statistic in small samples.

Presents (h, ø)‐entropies as a generalization of ø‐entropies. Studies some applications of this function in Bayesian inference, especially in the comparison of experiments. Also studies the relationship of the (h,ø)‐entropy criterion to the classical approaches of Blackwell (1951) and Lehmann (1959).

In this paper on the basis of the f*‐Divergence, a comparison criterion between fuzzy Information Systems is presented. This criterion is called “f*‐Divergence Criterion”.

On the basis of the f*‐Divergence for fuzzy information systems, this article presents a sequential selection method for a fixed number of fuzzy systems. f*‐Divergence is a measure of the quantity of information concerning the state space provided by the fuzzy system when the a priori probability distribution is defined on the space. The method described by the author determines a procedure which maximises the “Terminal” f*‐Divergence.

The decision rule which minimizes the probability of error, in the discrimination problem, is the Bayes decision rule which assigns x to the class with the highest a posteriori probability. This rule leads to a partial probability of error which is given by Pe(x) = 1−max p(C2lx) for each x e X. Prior to observing X, the probability of error associated with X is defined as Pe = EX [Pe(x)]. Tanaka, Okuda and Asai formulated the discrimination problem with fuzzy classes and fuzzy information using the probability of fuzzy events and derived a bound for the average error probability, when the decision in the classifier is made according to the fuzzified Bayes method. The aim is to obtain bounds for the average error probability in terms of (αβ)‐information energy, when the decision in the classifier is made according to the fuzzified Bayes method.

Weighted (h,φ) – divergence statistics are obtained by either replacing both distributions involved in the argument by their nonparametric estimators or replacing one distribution and considering the other as given. Asymptotic properties of weighted (h,φ) – divergence statistics are obtained and some tests constructed on the basis of these results are presented.

Goodness‐of‐fit test based on K_ϕ‐divergence between observed and theoretical frequencies are considered. The asymptotic chi‐square null distribution and three alternative approximations to the exact distribution function of this family are compared in small samples. Numerical results are presented for the symmetric null hypothesis for different multinomial sample sizes with various cell numbers. Exact power under specific alternatives to the symmetric null hypothesis are calculated and a comparison with the family of power divergence statistics is made.

Transport policy is constrained by the dilemma of the positive impacts of lowering the generalised costs of travel and their today non-ignorable negative externalities. This chapter details this dilemma and discusses current policy ideas to manage and overcome it against the impacts of the COVID-19 pandemic on travel habits and work behaviour. The impacts are presented for Switzerland for which a large-scale GPS tracking survey spanning the autumn 2019 to winter 2021 period is available. The chapter concludes by highlighting the dilemma of transport policy by discussing a number of potential solutions for the future.

Proposes a test of goodness‐of‐fit with composite null hypotheses and weights in the classes based on weighted (h,φ)‐divergences.

The weighted (h,φ)‐divergence between an empirical distribution and the probability of the estimated model is here investigated for large simple random samples.

The unknown parameters of the model are estimated using minimum (h,φ)‐divergences estimators with weights as studied in previous works by the authors.

Research makes an important contribution to (h,φ)‐divergences and their applications in statistical and other areas.