The bimodal standard normal density and kurtosis

نویسندگان
Behboodian, Javad ID 1
Sharafi, Maryam ID 2
Sajjadnia, Zahra ID 3
Zarepour, Mazyar ID 4

1 Department of Statistics, School of Science, Shiraz University, Shiraz, Iran

2 Department of Statistics, School of Science, Shiraz University, Shiraz, Iran

3 Department of Statistics, School of Science, Shiraz University, Shiraz, Iran

4 Department of Mathematics, Islamic Azad University, Shiraz Branch, Shiraz, Iran

doi
10.22060/ajmc.2018.3040
چکیده

 In this article, first a density by the name ”The bimodal standard normal density” is introduced and denoted by $b\varphi(z)$. Then, a definition for the kurtosis of bimodal densities relative to $b\varphi(z)$ is presented. Finally, to illustrate the introduced kurtosis, a few examples are provided and a real data set is studied, too.

کلیدواژه‌ها
normal density, mixed normal density, bimodal standard normal density, kurtosis of a bimodal density