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Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 22, No. 1, pp. 113-119 (2006)
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# On monotonic behaviour of relative increments of unimodal distributions

## Zoltán Szabó

Sultan Qaboos University, Oman

**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

**Full text of the article:**

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© 2006 ELibM and
FIZ Karlsruhe / Zentralblatt MATH
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