The recent discoveries of new forms of quantum statistics require a close look at the underlying Fock space structure. This exercise becomes all the more important in order to provide a general classification scheme for various forms of statistics, and establish interconnections among them whenever it is possible. We formulate a theory of generalized Fock spaces, which has a three tired structu...

In this paper, new recurrence relations satisfied by the single and product moments using moment generating function of dual generalized order statistics from inverse exponential-type distribution are established. Recurrence relations for single and product moments of reversed order statistics and lower record value are obtained as special cases. Further, using a recurrence relation for single ...

Normally the mass of a root has a uniform distribution but some of have different uniform distribution named generalized uniform distribution (GUD). The characterization result based on expectation of function of order statistics has been obtained for generalized uniform distribution. Applications are given for illustrative purpose.

A generalized notion of higher order nonclassicality (in terms of higher order moments) is introduced. Under this generalized framework of higher order nonclassicality, conditions of higher order squeezing and higher order subpoissonian photon statistics are derived. A simpler form of the Hong-Mandel higher order squeezing criterion is derived under this framework by using an operator ordering ...

This paper presents a generalized i-vector framework with phonetic tokenizations and tandem features for speaker verification as well as language identification. First, the tokens for calculating the zero-order statistics is extended from the MFCC trained Gaussian Mixture Models (GMM) components to phonetic phonemes, 3-grams and tandem feature trained GMM components using phoneme posterior prob...

Generalized quantum statistics such as para-Fermi statistics is characterized by certain triple relations which, in the case of para-Fermi statistics, are related to the orthogonal Lie algebra Bn = so(2n + 1). In this paper, we give a quite general definition of “a generalized quantum statistics associated to a classical Lie algebra G”. This definition is closely related to a certain Z-grading ...

This paper mainly studies the order statistics of geometric distribution. The deduces joint frequency function and conditional statistics, and, obtain prove some important propositions Certain are different from also similar to corresponding exponential distribution.