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Table 1 Types of Pearson distributions

From: Computing and graphing probability values of pearson distributions: a SAS/IML macro

Typeκ-CriterionDensity functionDomain
Main Type
Iκ<0\(f(x)=y_{0}(1+\frac {x}{a_{1}})^{m_{1}}(1-\frac {x}{a_{2}})^{m_{2}}\)a1xa2
IV0<κ<1\(\phantom {\dot {i}\!}f(x)=y_{0}(1+\frac {x^{2}}{a^{2}})^{-m}e^{-\nu \arctan (x/a)}\)<x<
VIκ>1\(f(x)=y_{0}(x-a)^{q_{2}}x^{-q_{1}}\phantom {\dot {i}\!}\)ax<
Transition Type
Normalκ=0(β2=3)\(\phantom {\dot {i}\!}f(x)=y_{0}e^{-x^{2}/(2\mu _{2})}\)<x<
IIκ=0(β2<3)\(f(x)=y_{0}(1-\frac {x^{2}}{a^{2}})^{m}\)axa
IIIκ\(f(x)=y_{0}(1+\frac {x}{a})^{\gamma {a}}e^{-\gamma {x}}\)ax<
Vκ=1f(x)=y0xpeγ/x0<x<
VIIκ=0(β2>3)\(f(x)=y_{0}(1+\frac {x^{2}}{a^{2}})^{-m}\)<x<