Immediately, we have the following result, which may be exploited for generating random variables from PHLD.
Note that when [alpha] = 1, we have the Truncated Half-Logistic Distribution; when [alpha] = 2, [alpha] = 1, it gives HLD; and when a = 2, [alpha] > 0, it gives PHLD.
where H(x) is the distribution function of PHLD or its generalizations and [phi](x) takes different forms of [bar.
Result number 3 of Table 4 is obtained by taking the [gamma] th power of distribution function of PHLD (called as Type I PHLD) which is the same as in Cordeiro et al.
When we use this data set for the four distributions, Weibull, Type I HLD, PHLD, and GPHLD, the results are as follows.
Results are illustrated in Table 7 and it is clear that PHLD is the most suitable for this data set.
Caption: FIGURE 1: pdfs of PHLD for various values of the parameters.
Caption: FIGURE 2: Comparison of PHLD, HLD, and Weibull densities.
Caption: FIGURE 3: Survival function of PHLD ([beta]= 0.
Caption: FIGURE 4: Hazard rate of PHLD ([beta] = 0.