We study the extreme value distribution of stochastic processes modeled by superstatistics. Classical extreme value theory asserts that (under mild asymptotic independence assumptions) only three possible limit distributions are possible, namely: Gumbel, Fréchet and Weibull distribution. On the other hand, superstatistics contains three important universality classes, namely χ-superstatistics, ...

Complex systems are frequently governed by a hierarchy of dynamics on different time scales. Superstatistics, which is a “statistics of statistics” with several largely separated time scales, aims to describe their nonequilibrium stationary states. Here, a prototype system, i.e., a Brownian particle moving through a fluctuating medium with slowly varying temperature, is considered, and a Fokker...

The $\kappa $ - notation="LaTeX">$\mu / inverse gamma and notation="LaTeX">$\eta composite fading models are presented extensively investigated in this paper. We derive closed-form expressions for the fundamental statistics of model, ...

For a sample of n independent identically distributed p-dimensional centered random vectors with covariance matrix Σn let S̃n denote the usual sample covariance (centered by the mean) and Sn the non-centered sample covariance matrix (i.e. the matrix of second moment estimates), where p > n. In this paper, we provide the limiting spectral distribution and central limit theorem for linear spectral...

Individual data from a continuous distribution are often partitioned into a collection of intervals defined by either fixed interval limits or sample quantiles. In this study, we derive asymptotic distribution of interval statistics for both cases, allowing multiple sample statistics for each interval. Under fixed intervals, the covariance matrix is singular. We identify a computationally simpl...

This article reports an extension of powered inverse Rayleigh distribution via DUS transformation, named DUS-Powered Inverse (DUS-PIR) distribution. Some statistical properties suggested in particular, moments, mode, quantiles, order statistics, entropy, inequality measures and stress-strength parameter have been investigated extensively. To estimate the parameters, maximum likelihood estimatio...

The Weibull-inverse exponential-loglogistic distribution which is abbreviated as (Weibull-IE-loglogistc) a member of the neotric T- inverse exponential family introduced previously by authors. Properties this such (mode, quantile function, median, hazard survival moments, order statistics and Shannon’s entropy) are derived, maximum likelihood estimates its parameters obtained. usefulness neoter...

Rayleigh distribution is one of the well-known continuous distribution developed by Lord Rayleigh and J.W. Strutt (1880, 1919) used in modeling lifetime data. A reciprocal transformation of Rayleigh variable generates inverse Rayleigh distribution derived by Voda (1972) which is also being used in lifetime experiments. While keeping in mind the famous of Rayleigh and inverse Rayleigh distributi...