TY - JOUR
T1 - On a New Bimodal Normal Family
TT - دربارهی خانوادهی نرمال دومدی جدید
JF - srtc-jsri
JO - srtc-jsri
VL - 8
IS - 2
UR - http://jsri.srtc.ac.ir/article-1-72-en.html
Y1 - 2012
SP - 163
EP - 176
KW - Double normal family
KW - standard double normal
KW - confidence interval
KW - point estimation
KW - pivotal quantity.
N2 - The unimodal distributions are frequently used in the theorical statistical studies. But in applied statistics, there are many situations in which the unimodal distributions can not be fitted to the data. For example, the distribution of the data outside the control zone in quality control or outlier observations in linear models and time series may require to be a bimodal. These situations, occur when the recorded data have the probability proportional to an increasing function of absolute value of deviations. In this paper a new family of distributions called double normal family of distribution is introduced and characterized. This symmetric family is a subclass of the univariate Kotz type distributions. The normal distribution is a special case of this family. Estimation of location and scale parameters by moment and maximum likelihood methods are given. Some pivotal quantity are introduced. Confidence intervals for some parameters by numerical methods are given.
M3 10.18869/acadpub.jsri.8.2.163
ER -