Η βαθμίδα αποτυχίας και ο μέσος υπολειπόμενος χρόνος ζωής για μείξεις κατανομών Erlang
The failure rate and mean residual life for mixtures of Erlang distributions
KeywordsΚατανομή Erlang ; Κυρτότητα ; Μονοτονία ; Βαθμίδα αποτυχίας ; Μέσος υπολειπόμενος χρόνος ζωής
The length of a lifetime could be described by the instantaneous probability of death and the expected remaining time until death. In particular, in the present dissertation we study failure rate and mean residual life under mixture of Erlang distributions. The distribution of time may be more precise under mixture of distributions than a single distribution. Moreover, the selection of Erlang distribution is based on its various applications, because the shape parameter is positive integer and the cumulative distribution function is easily manipulated compared with Gamma distribution. Our aim is to distinguish and study relationships between the two functions and also whether some characteristics work under mixture, such as monotonicity, kurtosis and measures of the distribution. Our main concern is to examine what combination of parameters and weights can lead to specific characteristics.