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Some properties of Bi-Weibull distributions

Ahmad Mahir Razali, Ali A. Al-Wakeel

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Abstract

In reliability, a Bi-Weibull distribution can be represented by a combination of two decreasing, constant or increasing failure rate functions. Several versions of Bi-Weibull distributions can be found but these versions differ in the way in which the two Weibull distributions were combined and in the number of parameters specified. In this paper we determine the Bi-Weibull distribution from a combination of two Weibull distributions each having 2 or 3-parameters. We also determine the probability density, cumulative distribution, survival and hazard functions of the 4, 5, and 6-parameter Bi-Weibull distributions. The result is that by increasing the number of parameters would give the distribution more flexibility. An application of the 4-parameter Bi-Weibull distribution is also included using real data

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What this paper is about

In reliability, a Bi-Weibull distribution can be represented by a combination of two decreasing, constant or increasing failure rate functions. Several versions of Bi-Weibull distributions can be found but these versions differ in the way in which the two Weibull distributions were combined and in the number of parameters specified. In this paper we determine the Bi-Weibull distribution from a combination of two Weibull distributions each having 2 or 3-parameters. We also determine the probability density, cumulative distribution, survival and hazard functions of the 4, 5, and 6-parameter Bi-Weibull distributions. The result is that by increasing the number of parameters would give the distribution more flexibility. An application of the 4-parameter Bi-Weibull distribution is also included using real data

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Available abstract

In reliability, a Bi-Weibull distribution can be represented by a combination of two decreasing, constant or increasing failure rate functions. Several versions of Bi-Weibull distributions can be found but these versions differ in the way in which the two Weibull distributions were combined and in the number of parameters specified. In this paper we determine the Bi-Weibull distribution from a combination of two Weibull distributions each having 2 or 3-parameters. We also determine the probability density, cumulative distribution, survival and hazard functions of the 4, 5, and 6-parameter Bi-Weibull distributions. The result is that by increasing the number of parameters would give the distribution more flexibility. An application of the 4-parameter Bi-Weibull distribution is also included using real data

Key concepts: Weibull distribution, Weibull modulus, Exponentiated Weibull distribution, Statistics, Weibull fading, Mathematics, Log-logistic distribution, Cumulative distribution function

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