It is pointed out that the case for Shannon entropy and von Neumann entropy, as measures of uncertainty in quantum mechanics, is not as bleak as suggested in quant-ph/0006087. The main argument of the latter is based on one particular interpretation of Shannon’s H-function (related to consecutive measurements), and is shown explicitly to fail for other physical interpretations. Further, it is s...

In many life-testing and reliability studies, the experimenter might not always obtain complete information on failure times for all experimental units. One of the most common censoring schemes is progressive type-II censoring. The aim of this paper is characterizing the parent distributions based on Shannon entropy of progressive type-II censored order statistics. It is shown that the equality...

In this paper, we obtain the Rényi entropy rate for irreducible-aperiodic Markov chains with countable state space, using the theory of countable nonnegative matrices. We also obtain the bound for the rate of Rényi entropy of an irreducible Markov chain. Finally, we show that the bound for the Rényi entropy rate is the Shannon entropy rate.

5 Information 15 5.1 Information As Surprise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 5.2 Average Shannon Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 5.3 How Surprised Should You Be? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 5.4 Entropy As Average Shannon Information . . . . . . . . . . . . . . . . . . . . . . 20 5.5 Dicing...

By replacing linear averaging in Shannon entropy with Kolmogorov-Nagumo average (KN-averages) or quasilinear mean and further imposing the additivity constraint, Rényi proposed the first formal generalization of Shannon entropy. Using this recipe of Rényi, one can prepare only two information measures: Shannon and Rényi entropy. Indeed, using this formalism Rényi characterized these additive en...

Past work shows that one can associate a notion of Shannon entropy to Dirichlet polynomial, regarded as an empirical distribution. Indeed, be extracted from any d:Dir by two-step process, where the first step is rig homomorphism out Dir, *set* polynomials, with structure given standard addition and multiplication. In this short note, we show upgraded *functor*, when replace set polynomials *cat...

We present a somewhat different way of looking on Shannon entropy. This leads to an axiomatisation of Shannon entropy that is essentially equivalent to that of Fadeev.