Pareto random variable

X is a Pareto random variable with parameters a,b if

fX(x)=abaxa+1, x[b,)


  • a(0,)

  • b(0,)




  1. 1.

    X represents a random variableMathworldPlanetmath with shape parameter a and scale parameter b.

  2. 2.

    The expected valueMathworldPlanetmath of X is noted as E[X]=aba-1 with a{2,3,}

  3. 3.

    The varianceMathworldPlanetmath of X is noted as Var[X]=ab2(a-1)2(a-2), a{3,4,}

  4. 4.

    The cumulative distribution functionMathworldPlanetmathPlanetmathPlanetmath of X is noted as F(x)=1-(bx)a

  5. 5.

    The moments of X around 0 are noted as E[Xn]=abna-n, n{1,2,,a-1}

Title Pareto random variable
Canonical name ParetoRandomVariable
Date of creation 2013-03-22 12:34:05
Last modified on 2013-03-22 12:34:05
Owner alozano (2414)
Last modified by alozano (2414)
Numerical id 9
Author alozano (2414)
Entry type Definition
Classification msc 62E15
Synonym Pareto distribution