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(a) Substituting the recurrence pn=(a+nb)pn1 for n2 into the PGF P(z).pdf

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(a) Substituting the recurrence pn=(a+nb)pn1 for n2 into the PGF P(z)=n=0pnzn and its derivatives, write down a differential equation satisfied by P(z). (b) Show that the PGF of a distribution from the (a,b,1) class is P(z)=1(1a)aa+b(1p0)(1a1az)aa+b+p0(1a)aa+b.

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(a) Substituting the recurrence pn=(a+nb)pn1 for n2 into the PGF P(z)=n=0pnzn and its derivatives, write down a differential equation satisfied by P(z). (b) Show that the PGF of a distribution from the (a,b,1) class is P(z)=1(1a)aa+b(1p0)(1a1az)aa+b+p0(1a)aa+b

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(a) Substituting the recurrence pn=(a+nb)pn1 for n2 into the PGF P(z).pdf

  • 1. (a) Substituting the recurrence pn=(a+nb)pn1 for n2 into the PGF P(z)=n=0pnzn and its derivatives, write down a differential equation satisfied by P(z). (b) Show that the PGF of a distribution from the (a,b,1) class is P(z)=1(1a)aa+b(1p0)(1a1az)aa+b+p0(1a)aa+b