On a New Bimodal Normal Family

author

Abstract:

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.

Upgrade to premium to download articles

Sign up to access the full text

Already have an account?login

similar resources

A New Skew-normal Density

We present a new skew-normal distribution, denoted by NSN($lambada$). We first derive the density and moment generating function of NSN($lambada$). The properties of SN($lambada$), the known skew-normal distribution of Azzalini, and NSN($lambada$) are compared with each other. Finally, a numerical example for testing about the parameter $lambada$ in NSN($lambada$) is given. ...

full text

Orbital Normal Forms for a family of-zero Singularity

Consider a Dynamical system x'=F(x,µ) such that its linear part has a pair of imaginary eigenvalues and one zero eigenvalue (Hopf zero singularity). Recently, the simplest normal form for this singular system has been obtained by sl(2) Lie algebra theory and the decomposition of space into three invariant subspaces. The normal form of this singular system is divided into three general cases. In...

full text

Note on the Normal Family

In this paper we consider the problem of normal family criteria and improve some results of I. Lihiri, S. Dewan and Y. Xu.

full text

A new family of (A, N)-implications: Construction and properties

This paper deals with a new family of (A, N)-implications that derived from fuzzy negation and continuous monotone function, and some properties, like the left neutrally, the exchange principle, the ordering property and the laws of contraposition, of the proposed family of (A, N)-implications are studied. Moreover, the T-conditionality and the Modus tollens for the new family of (A, N)-i...

full text

T-normal family of distributions: a new approach to generalize the normal distribution

The idea of generating skewed distributions from normal has been of great interest among researchers for decades. This paper proposes four families of generalized normal distributions using the T -X framework. These four families of distributions are named as T -normal families arising from the quantile functions of (i) standard exponential, (ii) standard log-logistic, (iii) standard logistic a...

full text

A New Distribution Family Constructed by Fractional Polynomial Rank Transmutation

In this study‎, ‎a new polynomial rank transmutation is proposed with the help of‎ ‎ the idea of quadratic rank transmutation mapping (QRTM)‎. ‎This polynomial rank‎ ‎ transmutation is allowed to extend the range of the transmutation parameter from‎ ‎  [-1,1] to [-1,k]‎‎. ‎At this point‎, ‎the generated distributions gain more&lrm...

full text

My Resources

Save resource for easier access later

Save to my library Already added to my library

{@ msg_add @}


Journal title

volume 8  issue 2

pages  163- 176

publication date 2012-03

By following a journal you will be notified via email when a new issue of this journal is published.

Keywords

Hosted on Doprax cloud platform doprax.com

copyright © 2015-2023