On Double Lindley Distribution and Some of its Properties

Figures & data

Figure 1. The probability density function of the DLD for various values of θ.

Figure 2. The cumulative distribution function of the DLD for different values of θ.

Figure 3. The hazard rate function of the DLD for various parameter values.

Table 1. Estimated values of the parameters for the EDLD and Laplace distribution with respective KSS, AIC, BIC, and AICc values for the rocket propellant data.

Estimates of the Parameters	Laplace ($\mu ,\sigma$)	EDLD($\theta , \mu ,\sigma$)
$\widehat{\theta }$	—	0.00058
$\widehat{\mu }$	12.75	14.202
$\widehat{\sigma }$	6.549	0.00192
KSS	0.1387	0.1288
AIC	146.675	141.983
BIC	148.667	144.97
AICc	147.381	143.483

Table 2. Estimated values of the parameters for the EDLD and Laplace distribution with respective KSS, AIC, BIC, and AICc values for the hardwood data.

Estimates of the Parameters	Laplace ($\mu ,\sigma$)	EDLD($\theta , \mu ,\sigma$)
$\widehat{\theta }$	—	0.000745
$\widehat{\mu }$	34.0	36.0535
$\widehat{\sigma }$	11.2465	0.00423
KSS	0.1264	0.0992
AIC	160.269	157.821
BIC	162.158	160.654
AICc	161.019	159.421

Table 3. Estimated values of the parameters for the EDLD and Laplace distribution with respective KSS, AIC, BIC, and AICc values for the cigarette sales and cancer rate data.

Estimates of the Parameters	Laplace ($\mu ,\sigma$)	EDLD($\theta , \mu ,\sigma$)
$\widehat{\theta }$	—	0.20632
$\widehat{\mu }$	20.32	19.8632
$\widehat{\sigma }$	3.5647	0.4003
KSS	0.16866	0.09265
AIC	263.962	259.053
BIC	267.53	264.406
AICc	264.254	259.653

Table 4. Estimates of the parameters and the corresponding bias and mean square error.

Sample Size	Parameters	Estimates	M.S.E	Bias
n = 100	θ	1.3459	15.8286	−0.6541
	μ	5.0376	0.0522	0.0376
	σ	1.9646	39.6627	−1.0354
n = 200	θ	1.8138	1.7342	−0.1862
	μ	5.0058	0.0015	0.0058
	σ	2.7688	2.6728	−0.2312
n = 500	θ	2.0877	0.3152	0.0877
	μ	5.0024	0.0002	0.0024
	σ	3.1651	1.1172	0.1651