%A 1017031015 Agustia Indriani
%T MOMENT, CUMULANT, AND CHARACTERISTIC FUNCTION
OF GENERALIZED LOGISTIC DISTRIBUTION TYPE IV
%X The generalized logistic distribution type IV is a generalized from standard
logistic distribution that has two shape parameter, ? and ?. Standard logistic
distribution is obtained from general logistic distribution therefore ? = 0 dan s = 1.
In this study discuss about charactristic of generalized logistic distribution type IV
especially moment, cumulant, and characteristic function. Mean and varians are
actually another special things which is called moment. Moment
are obtained
by derivating moment generating function as many as r times. Although cumulant
is obtained by derivating cumulant generating function as many as r times.
Therefore cumulant generating function is obtained by using logarithm natural on
moment generating function. Moreover cumulant can be used to find skewness
and kurtosis from generalized logistic distribution type IV. Characteristic function
is one of transformation type that often be used on probability theory.
Characteristic function is obtain from expection value of therefore i is
imaginary unit and . Then from characteristic function that has been
obtained is proof that absolute value from characteristic function is equal 1. It is
show that generalized logistic distribution type IV has monotonic function.
Finally, the probability density function, skewness, and kurtosis were simulated
by mathlab to know whether it is increasing monotonic or decreasing monotonic.
Keywords : Generalized Logistic Distribution Type IV, Moment, Cumulant,
Characteristic Function
%C Universitas Lampung
%D 2014
%I Fakultas Mipa
%L eprints4059