This article introduces an extension of the Power Muth (PM) distribution for modeling
positive data sets with a high coefficient of kurtosis. The resulting distribution has greater kurtosis
than the PM distribution. We show that the density can be represented based on the incomplete
generalized integro-exponential function. We study some of its properties and moments, and its
coefficients of asymmetry and kurtosis. We apply estimations using the moments and maximum
likelihood methods and present a simulation study to illustrate parameter recovery. The results of
application to two real data sets indicate that the new model performs very well in the presence
of outliers.