The Gompertz Inverse Exponential (GoIE) distribution with applications

Figures & data

Figure 1. PDF of the GoIE distribution.

Figure 2. CDF of the GoIE distribution.

Figure 3. Reliability function of GoIE distribution.

Figure 4. Failure rate of the GoIE distribution.

Table 1. Table of result

Models	Estimates	NLL	AIC	CAIC	BIC	HQIC	Rank
GoIE (Proposed)	$\begin{array}{c}\stackrel{\wedge }{\alpha }=0.2030548\\ \stackrel{\wedge }{\beta }=11.5541435\\ \stackrel{\wedge }{\theta }=2.0003185\end{array}$	14.04093	34.08187	34.48865	40.51127	36.61059	1
GoExp (New)	$\begin{array}{c}\stackrel{\wedge }{\alpha }=-0.004768848\\ \stackrel{\wedge }{\beta }=-1.810999364\\ \stackrel{\wedge }{\theta }=-1.987714978\end{array}$	14.81765	35.6353	36.04208	42.06471	38.16402	2
GoWei (New)	$\begin{array}{c}\stackrel{\wedge }{\alpha }=0.228488761\\ \stackrel{\wedge }{\beta }=0.009628097\\ \stackrel{\wedge }{\theta }=0.794918813\\ \stackrel{\wedge }{\lambda }=5.612111282\end{array}$	15.18847	38.37694	39.06659	46.94948	41.74856	4
GoLom (Developed by Oguntunde et al. [2017])	$\begin{array}{c}\stackrel{\wedge }{\alpha }=0.004592168\\ \stackrel{\wedge }{\beta }=8.179090955\\ \stackrel{\wedge }{\theta }=0.506999370\\ \stackrel{\wedge }{\lambda }=1.515829085\end{array}$	14.50274	37.00548	37.69513	45.57802	40.3771	3

Figure 5. Histogram of the first data with the competing distributions.

Figure 6. The empirical cdf of the first data together with the competing distributions.

Table 2. Table of result

Models	Estimates	NLL	AIC	CAIC	BIC	HQIC	Rank
GoIE (Proposed)	$\begin{array}{c}\stackrel{\wedge }{\alpha }=4.636970\\ \stackrel{\wedge }{\beta }=1.583631\\ \stackrel{\wedge }{\theta }=25.794220\end{array}$	629.335	1264.67	1234.791	1274.595	1268.686	1
GoExp (New)	$\begin{array}{c}\stackrel{\wedge }{\alpha }=5.330925317\\ \stackrel{\wedge }{\beta }=20.978768343\\ \stackrel{\wedge }{\theta }=0.004836174\end{array}$	663.8036	1333.607	1333.728	1343.532	1337.623	4
GoWei (New)	$\begin{array}{c}\stackrel{\wedge }{\alpha }=11.22264866\\ \stackrel{\wedge }{\beta }=-1.29977338\\ \stackrel{\wedge }{\theta }=0.02630932\\ \stackrel{\wedge }{\lambda }=2.54531004\end{array}$	641.4217	1290.843	1291.046	1304.076	1296.197	2
GoLom (Developed by Oguntunde et al. [2017])	$\begin{array}{c}\stackrel{\wedge }{\alpha }=0.006519876\\ \stackrel{\wedge }{\beta }=3.370057658\\ \stackrel{\wedge }{\theta }=0.714843759\\ \stackrel{\wedge }{\lambda }=0.747124582\end{array}$	645.6623	1299.325	1299.528	1312.558	1304.679	3

Figure 7. Histogram of the second data with the competing distributions.

Figure 8. The empirical cdf of the second data together with the competing distributions.

Oguntunde, P. E., Khaleel, M. A., Ahmed, M. T., Adejumo, A. O., & Odetunmibi, O. A. 2017. A new generalization of the Lomax distribution with increasing, decreasing and constant failure rate. Article ID 6043169 Modelling and Simulation in Engineering, 2017, 6. doi:10.1155/2017/6043169

 Web of Science ®Google Scholar