Abstract
In this paper, we propose a new lifetime distribution. We discuss several mathematical properties of the new distribu- tion. Certain characterizations of the new distribution are provided. We study the maximum likelihood estimation and asymptotic interval estimation of the unknown parameters. A simulation study, as well as an application of the new distribution to failure data, are also presented. We end the paper with a number of remarks.
Highlights
Lifetime distributions play important roles in modeling and analysis of many life phenomena
We plotted the pdf and hrf of the inverted Nadarajah-Haghighi (INH) distribution and observed that they both are increasing-decreasing, see Figure 3
We can state that the ordinary moments (i.e. E(Xr) for r = 1, 2, 3, · · · ) of the transmuted inverted NadarajahHaghighi (TINH) distribution do not exist for all combinations of the parameters
Summary
Lifetime distributions play important roles in modeling and analysis of many life phenomena. We use the transmutation map to generalize the INH distribution To this end, we take g(x) and G(x) in (2) to be the pdf and cdf of the INH distribution, respectively, to obtain the pdf of the transmuted inverted NadarajahHaghighi (TINH) distribution as follows αβ βα f (x) = x2. Tahir et al (2018) claimed that the pdf and hrf of the INH distribution can be decreasing and they plotted pdf and hrf when the scale and shape parameters of the INH distribution set equal to one and 0.4, respectively, to show their claim. We plotted the pdf and hrf of the INH distribution (recall that INH is a special case of TINH when λ = 0) and observed that they both are increasing-decreasing, see Figure 3.
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