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We propose a new kernel estimation of the cumulative distribution function based on transformation and on bias reducing techniques. We derive the optimal bandwidth that minimises the asymptotic integrated mean squared error. The simulation results show that our proposed kernel estimation improves alternative approaches when the variable has an extreme value distribution with heavy tail and the sample size is small.

In most studies related to wind energy, the quantity of the air density is considered constant, but actually, we know that it is variable and depending on others natural factors. We present a new procedure to estimate the wind density power energy by simulating the components of the air density. The procedure uses the copula theory and demonstrates that the estimated power energy is higher if the air density is not constant.

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