6533b862fe1ef96bd12c6050
RESEARCH PRODUCT
Is there an absolutely continuous random variable with equal probability density and cumulative distribution functions in its support? Is it unique? What about in the discrete case?
Ernesto J. Veres-ferrerJosem Paviasubject
Characteristic function (probability theory)Cumulative distribution functionCalculusProbability mass functionProbability distributionApplied mathematicsProbability density functionMoment-generating functionRandom variableLaw of the unconscious statisticianMathematicsdescription
This paper inquires about the existence and uniqueness of a univariate continuous random variable for which both cumulative distribution and density functions are equal and asks about the conditions under which a possible extrapolation of the solution to the discrete case is possible. The issue is presented and solved as a problem and allows to obtain a new family of probability distributions. The different approaches followed to reach the solution could also serve to warn about some properties of density and cumulative functions that usually go unnoticed, helping to deepen the understanding of some of the weapons of the mathematical statistician’s arsenal.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2014-06-02 | International Journal of Advanced Statistics and Probability |