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mixture gamma and Weibull distribution.

Fig. 1 Normal mixture, Gamma and skewed Normal approximation for a distribution with a relatively simple shape.

Tian Pau [15] employed mixture gamma and Weibull distribution (GW) which is a combination of gamma and Weibull distributions, and also mixture normal distribution (NN) which is a mixture function of two-component truncated normal distribution for wind speed modeling.

Many PDFs have been proposed in recent past, but in present study Weibull, Lognormal, gamma, GEV, WW-PDF, mixture gamma and Weibull distribution, mixture normal distribution, mixture normal and Weibull distribution, and three new mixture distributions, viz., Weibull-lognormal, GEV-lognormal, and Weibull-GEV are used to describe wind speed characteristics.

The probability density function and cumulative distribution function of the mixture gamma and Weibull distribution are given by [15] h v ; α, β, k, c, w = w g v ; α, β + 1 − w f v ; k, c Open image in new window (17) H v ; α, β, k, c, w = w G v ; α, β + 1 − w F v ; k, c Open image in new window (18).

Results show that mixture probability functions are better alternatives to conventional Weibull, two-component mixture Weibull, gamma, and lognormal PDFs to describe wind speed characteristics.

Similar results can be observed under Uniform, Gamma, mixture of Gamma and Normal, and complex distribution (Figure 2C 2F).

The gamma and exponential mixtures both fit poorly (Δ DIC > 7).

In this section, extensive computer simulation results are presented to illustrate the performance of the CPF, CPF with BS, GML [8], and EML [8] approaches for estimating the clock offset in wireless sensor networks, assuming a variety of random network delay models such as asymmetric Gaussian, exponential, Gamma, and Weibull as well as a mixture of Gamma and Weibull, respectively.

Panel (a) shows a simple histogram of expression levels from the probe set, across all samples; Panel (b) shows the derived probability distribution, based on the Gamma Mixture hypothesis; and Panel (c) plots the probability of being in an Up state, as a function of the expression level.

The robustness of intervals to violations of the normality assumption was evaluated by generating effects and errors from uniform, mixture normal, and gamma distributions.