On the Maximal Lévy-Ottaviani Inequality for Sums of Independent and Dependent Random Vectors
We prove that the sums of independent random vectors satisfy , t ≥ 0.
On the micture of some sontinuous distributions
On the minimizing point of the incorrectly centered empirical process and its limit distribution in nonregular experiments
Let be the empirical distribution function (df) pertaining to independent random variables with continuous df . We investigate the minimizing point of the empirical process , where is another df which differs from . If and are locally Hölder-continuous of order at a point our main result states that converges in distribution. The limit variable is the almost sure unique minimizing point of a two-sided time-transformed homogeneous Poisson-process with a drift. The time-transformation...
On the minimizing point of the incorrectly centered empirical process and its limit distribution in nonregular experiments
Let Fn be the empirical distribution function (df) pertaining to independent random variables with continuous df F. We investigate the minimizing point of the empirical process Fn - F0, where F0 is another df which differs from F. If F and F0 are locally Hölder-continuous of order α at a point τ our main result states that converges in distribution. The limit variable is the almost sure unique minimizing point of a two-sided time-transformed homogeneous Poisson-process with a drift. The time-transformation...
On the multivariate skew-normal distribution and its scale mixtures.
On the number of local extrema in a sequence of independent random variables
On the number of word occurrences in a semi-Markov sequence of letters
Let a finite alphabet Ω. We consider a sequence of letters from Ω generated by a discrete time semi-Markov process We derive the probability of a word occurrence in the sequence. We also obtain results for the mean and variance of the number of overlapping occurrences of a word in a finite discrete time semi-Markov sequence of letters under certain conditions.
On the paradox of n random variables
On the probability that integers chosen according to the binomial distribution are relative prime
On the product and ratio of Bessel random variables.
On the product and ratio of Laplace and Bessel random variables.
On the properties of the Generalized Normal Distribution
The target of this paper is to provide a critical review and to enlarge the theory related to the Generalized Normal Distributions (GND). This three term (position, scale shape) distribution is based in a strong theoretical background due to Logarithm Sobolev Inequalities. Moreover, the GND is the appropriate one to support the Generalized entropy type Fisher's information measure.
On the quadratic Wiener functional associated with the Malliavin derivative of the square norm of Brownian sample path on interval.
On the rate of growth of Lev́y processes with no positive jumps conditioned to stay positive.
On the Rate of Growth of the Partial Maxima of a Sequence of Independent Identically Distributed Random Variables.
On the ratio of Pearson type VII and Bessel random variables.
On the relationship between Menger spaces and Wald spaces
On the robustness of properties characterizing the normal distribution
On the sharpened Heisenberg-Weyl inequality.
On the spectrum of a distribution function and on unique factorization.