:: Volume 8, Issue 2 (3-2012) ::
JSRI 2012, 8(2): 163-176 Back to browse issues page
On a New Bimodal Normal Family
Mohammad Reza Alavi *
, alavi_m@scu.ac.ir
Abstract:   (3094 Views)

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.

Keywords: Double normal family, standard double normal, confidence interval, point estimation, pivotal quantity.
Full-Text [PDF 210 kb]   (1289 Downloads)    
Type of Study: Research | Subject: General
Received: 2015/12/30 | Accepted: 2015/12/30 | Published: 2015/12/30

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Volume 8, Issue 2 (3-2012) Back to browse issues page