Abstract: Sufficient conditions for monotonic behaviour of relative increment and hazard rate functions h of unimodal distributions of types U and J are being investigated, proved and then applied to some distributions. In addition, a general algorithm for checking monotonic properties of h is given, where we do not need the cumulative distribution function. Instead, we use the probability density function f and its first two derivatives only.
Keywords: Distribution function, density function, hazard rate, relative increment function.
Classification (MSC2000): 60E99; 62N05, 62P99
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