Division of distributions

Systems of Division Problems for Distributions

Suppose (ftj)ist.jtr is a pxp matrix of real-valued infinitely (respectively /«-times continuously) differentiable functions on an open subset fl of R". Then (fti)isi,isp maps the space of ^-tuples of distributions on fl (respectively distributions of order Smonfi) into itself. In the present paper, the pxp matrices (P/)isi,<sp for which this mapping is onto are characterized in terms of the ze...

The division problem for tempered distributions of one variable

We give a characterization, in one variable case, of those C∞ multipliers F such that the division problem is solvable in S′(R). For these functions F ∈ OM (R) we even prove that the multiplication operator MF (G) = FG has a continuous linear right inverse on S′(R), in contrast to what happens in the several variables case, as was shown by Langenbruch. 2010 Mathematics Subject Classification. P...

Triangulaizability of Algebras Over Division Rings

A Method to Expand Family of Continuous Distributions based on Truncated Distributions

&nbsp;Abstract: A new method to generate various family of distributions is introduced. This method introduces a new two-parameter extension of the exponential distribution to illustrate its application. Some statistical and reliability properties of the new distribution, including explicit expressions for the moments, quantiles, mode, moment generating function, mean residual lifetime, stochas...

Classification and properties of acyclic discrete phase-type distributions based on geometric and shifted geometric distributions

Acyclic phase-type distributions form a versatile model, serving as approximations to many probability distributions in various circumstances. They exhibit special properties and characteristics that usually make their applications attractive. Compared to acyclic continuous phase-type (ACPH) distributions, acyclic discrete phase-type (ADPH) distributions and their subclasses (ADPH family) have ...