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Characterization of a class of lifetime distributions

Knopik L.

Control and Cybernetics

2006

Vol. 35, no 2

407-414

In Knopik (2005) the ageing class MTFR (Mean Time to Failure or Repair) of lifetime distribution was introduced. In this paper, we show that the family MTFR is closed under weak convergence of distribution and convolution. We prove that the dual family MTFR^D (in a particular case) is closed under mixtures.

On the characterization of the exponential distribution by record values with a random index

Iwińska M.

Fasciculi Mathematici

2005

Nr 36

33-39

We give some characterizations of the exponential distribution based on the distributional properties and the expected values of record values; the index of record values has the geometric distribution.

Some results on the ageing class

Knopik L.

Control and Cybernetics

2005

Vol. 34, no 4

1175-1180

In this paper, we investigate an ageing class of life distributions. We show that the family of life distributions is closed under formation of parallel and series systems. This class is situated between IFR and NBUE.

On the characterization of the exponential distribution by expected value of record value with random index

Iwińska M.

Fasciculi Mathematici

1998

Nr 28

57-61

In this paper we give some characterizations of the exponential distribution based on the expected value of record value. These characterizations are considered for distribution functions belonging to IFRA or DFRA. The index of record value has the geometric distribution.