A bivariate conditional Weibull distribution with application


A three-parameter bivariate distribution is derived from the marginal and conditional Weibull distributions. Its joint properties are derived and method of estimation of its parameters discussed. It is generalised for the multivariate case when the assumptions of piecewise conditional independence of the variables is tenable. It is applied to a bivariate data set of wind speed and solar radiation, where the conditional dependence of the two variables involved is suspected. The result shows that the model is compatible with the data. It is proposed for application when there is need to allow for such conditional structure in a bivariate model.

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See Tables 3 and 4.

Table 3 Daily solar radiation (MJ/m2) at Yola in 2015
Table 4 Daily wind speed (m/s) at Yola in 2015

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Gongsin, I.E., Saporu, F.W.O. A bivariate conditional Weibull distribution with application. Afr. Mat. 31, 565–583 (2020). https://doi.org/10.1007/s13370-019-00742-8

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  • Bivariate conditional Weibull distribution
  • Newton–Raphson method
  • Joint moments
  • Hessian matrix

Mathematics Subject Classification

  • 742