Goodness-of-fit tests for Laplace, Gaussian and exponential power distributions based on <i>λ</i>-th power skewness and kurtosis
نویسندگان
چکیده
Temperature data, like many other measurements in quantitative fields, are usually modeled using a normal distribution. However, some distributions can offer better fit while avoiding underestimation of tail event probabilities. To this point, we extend Pearson's notions skewness and kurtosis to build powerful family goodness-of-fit tests based on Rao's score for the exponential power distribution $\mathrm{EPD}_{\lambda}(\mu,\sigma)$, including normality Laplacity when $\lambda$ is set 1 or 2. We find asymptotic our test statistic, which sum squares two $Z$-scores, under null local alternatives. also develop an innovative regression strategy obtain $Z$-scores that nearly independent distributed as standard Gaussians, resulting $\chi_2^2$ valid any sample size (up very high precision $n\geq 20$). The case $\lambda=1$ leads Laplace($\mu,\sigma$) distribution, whose empirical superior all $39$ competitors literature, over wide range $400$ Theoretical proofs particularly challenging substantial. applied three temperature datasets. new implemented R package PoweR.
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ژورنال
عنوان ژورنال: Statistics
سال: 2022
ISSN: ['1029-4910', '0233-1888', '1026-7786']
DOI: https://doi.org/10.1080/02331888.2022.2144859