On the mixture proportional mean residual life model. (English) Zbl 1332.62217
Summary: In this article, we propose a new mixture model induced by the model of proportional mean residual life. Under some appropriate assumptions, it is shown that the mixing and overall variables in the model admit the positive likelihood ratio dependence structure. To see how the overall variable is affected by the stochastic variation of the mixing variable, we study some stochastic comparisons using these variables. Finally, some useful bounds for tail probability of the overall variable for large values of the mixing variable are derived.
MSC:
| 62H30 | Classification and discrimination; cluster analysis (statistical aspects) |
| 62N05 | Reliability and life testing |
References:
| [1] | Barlow R., Statistical Theory of Reliability and Life Testing Probability Models (1975) · Zbl 0379.62080 |
| [2] | DOI: 10.1016/j.jspi.2012.07.020 · Zbl 1428.62454 · doi:10.1016/j.jspi.2012.07.020 |
| [3] | DOI: 10.1080/02331889808802660 · Zbl 0916.62064 · doi:10.1080/02331889808802660 |
| [4] | DOI: 10.1016/j.jspi.2005.02.020 · Zbl 1093.62096 · doi:10.1016/j.jspi.2005.02.020 |
| [5] | DOI: 10.1080/03610928708829408 · Zbl 0609.62092 · doi:10.1080/03610928708829408 |
| [6] | DOI: 10.1016/0167-7152(94)00056-E · Zbl 0813.62009 · doi:10.1016/0167-7152(94)00056-E |
| [7] | Karlin S., Total Positivity (1968) |
| [8] | Lai C.D., Stochastic Ageing and Dependence for Reliability (2006) · Zbl 1098.62130 |
| [9] | Li X., Probab. Eng. Inform. Sci. 44 (20) pp 479– (2006) |
| [10] | DOI: 10.1016/S0378-3758(02)00157-X · Zbl 1016.62060 · doi:10.1016/S0378-3758(02)00157-X |
| [11] | DOI: 10.1016/j.spl.2005.10.019 · Zbl 1089.62120 · doi:10.1016/j.spl.2005.10.019 |
| [12] | DOI: 10.1109/TR.2009.2035791 · doi:10.1109/TR.2009.2035791 |
| [13] | Nelsen R.B., An Introduction to Copulas (2006) |
| [14] | DOI: 10.1007/978-0-387-34675-5 · Zbl 1111.62016 · doi:10.1007/978-0-387-34675-5 |
| [15] | DOI: 10.1016/j.jspi.2007.04.029 · Zbl 1133.62088 · doi:10.1016/j.jspi.2007.04.029 |
| [16] | DOI: 10.1016/0378-3758(92)90135-F · doi:10.1016/0378-3758(92)90135-F |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
