Journal of Statistics Applications & Probability

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In this article, we developed a new statistical model named as the generalized complementary exponentiated Bell-Touchard model. The exponential model is taken as a special baseline model with a configurable failure rate function. The proposed model is based on several features of zero-truncated Bell numbers and Touchard polynomials that can address the complementary risk matters. The linear representation of the density of the proposed model is provided that can be used to obtain numerous important properties of the special model. The well-known actuarial metrics namely value at risk and expected shortfall are formulated, computed and graphically illustrated for the sub model. The maximum likelihood approach is used to estimate the parameters. Furthermore, we designed the group acceptance sampling plan for the proposed model by using the median as a quality parameter for truncated life tests. Three real data applications are offered for the complementary exponentiated Bell Touchard exponential model. The analysis of the two failure times data and comparative study yielded optimized results of the group acceptance sampling plan under the proposed model. The application to insurance claim data also provided the best results and showed that the proposed model had heavier tail.

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