| Citation: |
Xiaoling Xu, Xinyi Xu, Beiqing Gu, Ronghua Wang. STUDY ON THE GENERALIZED THREE-PARAMETER LINDLEY DISTRIBUTION[J]. Journal of Applied Analysis & Computation, 2024, 14(6): 3581-3609. doi: 10.11948/20240136
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STUDY ON THE GENERALIZED THREE-PARAMETER LINDLEY DISTRIBUTION
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Abstract
This paper introduces a new life distribution, the generalized three-parameter Lindley distribution, derived as a product of the inverse power law model and the generalized two-parameter Lindley distribution in a progressive stress accelerated life testing scenario. The study presents the graphical characteristics of the density function, failure rate function, mean failure rate function, and mean residual life function. Point estimates for the three parameters are provided through logarithmic transformation. The paper concludes with two practical examples demonstrating the application of this method.
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References
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Xiaoling Xu, Xinyi Xu, Beiqing Gu, Ronghua Wang. STUDY ON THE GENERALIZED THREE-PARAMETER LINDLEY DISTRIBUTION[J]. Journal of Applied Analysis & Computation, 2024, 14(6): 3581-3609. doi: 10.11948/20240136
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Figure 1.
Graph of
$ \beta_{0} $ $ m(0.5 \leq m \leq 1) $ -
Figure 2.
Graph of the density function with
$ m=0.1, \beta=0.5, \theta=1 $ -
Figure 3.
Graph of the density function with
$ m=0.4, \beta=0.5, \theta=1 $ -
Figure 4.
Graph of the density function with
$ m=0.8, \beta=0.5, \theta=1 $ $ (\beta_{0}=0.8, \frac{m}{3 m-1}=\frac{4}{7} ) $ -
Figure 5.
Graph of the density function with
$ m=0.8, \beta=0.6, \theta=1 $ $ (\beta_{0}=0.8, \frac{m}{3 m-1}=\frac{4}{7} ) $ -
Figure 6.
Graph of the density function with
$ m=0.8, \beta=0.85, \theta=1 $ $ (\beta_{0}=0.8, \frac{m}{3 m-1}=\frac{4}{7} ) $ -
Figure 7.
Graph of the density function with
$ m=1.5, \beta=0.5, \theta=1 $ -
Figure 8.
Graph of the failure rate function with
$ m=0.1, \beta=0.5, \theta=1 $ -
Figure 9.
Graph of the failure rate function with
$ m=0.8, \beta=0.2, \theta=1 $ -
Figure 10.
Graph of the failure rate function with
$ m=0.8, \beta=1, \theta=1 $ -
Figure 11.
Graph of the failure rate function with
$ m=0.8, \beta=0.6, \theta=1 $ -
Figure 12.
Graph of the failure rate function with
$ m=0.8, \beta=0.8, \theta=1 $ -
Figure 13.
Graph of the failure rate function with
$ m=1.5, \beta=0.5, \theta=1 $ -
Figure 14.
Graph of the mean failure rate function with
$ m=0.1, \beta=0.5, \theta=1 $ -
Figure 15.
Graph of the mean failure rate function with
$ m=0.8, \beta=0.2, \theta=1 $ -
Figure 16.
Graph of the mean failure rate function with
$ m=0.8, \beta=0.5, \theta=1 (\beta_0=0.656402) $ -
Figure 17.
Graph of the mean failure rate function with
$ m=0.8, \beta=0.66, \theta=1 (\beta_0=0.656402) $ -
Figure 18.
Graph of the mean failure rate function with
$ m=0.8, \beta=0.67, \theta=1 (\beta_0=0.656402) $ -
Figure 19.
Graph of the mean failure rate function with
$ m=0.8, \beta=0.68, \theta=1 (\beta_0=0.656402) $ -
Figure 20.
Graph of the mean failure rate function with
$ m=0.8, \beta=0.685, \theta=1 (\beta_0=0.656402) $ -
Figure 21.
Graph of the mean failure rate function with
$ m=0.8, \beta=0.69, \theta=1 (\beta_0=0.656402) $ -
Figure 22.
Graph of the mean failure rate function with
$ m=0.8, \beta=0.7, \theta=1 (\beta_0=0.656402) $ -
Figure 23.
Graph of the mean failure rate function with
$ m=1.5, \beta=0.5, \theta=1 $ -
Figure 24.
Graph of the mean residual life with
$ m=0.1, \beta=0.5, \theta=1 $ -
Figure 25.
Graph of the mean residual life with
$ m=0.8, \beta=0.3, \theta=1 $ -
Figure 26.
Graph of the mean residual life with
$ m=0.8, \beta=0.5, \theta=1 $ -
Figure 27.
Graph of the mean residual life with
$ m=0.8, \beta=0.65, \theta=1 $ -
Figure 28.
Graph of the mean residual life with
$ m=0.8, \beta=0.7, \theta=1 $ -
Figure 29.
Graph of the mean residual life with
$ m=0.8, \beta=1, \theta=1 $ -
Figure 30.
Graph of the mean residual life with
$ m=1.5, \beta=0.5, \theta=1 $ -
Figure 31.
Empirical distribution function and theoretical distribution functions for case 6.1.
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Figure 32.
Empirical distribution function and theoretical distribution functions for case 6.2.