Natural exponential family

About: Natural exponential family is a research topic. Over the lifetime, 1973 publications have been published within this topic receiving 60189 citations. The topic is also known as: NEF.

Minimax posterior regret actions for exponential families of distributions and weighted squared error loss

Abstract: The paper focuses on the choice of appropriate loss in a Bayesian framework. In particular, a criterion based on minimax posterior regret is considered. Attention is paid to classes of weighted squared error loss. A general result is presented and an application to one parameter exponentia families of distributions is given.

Fitting probability distributions to market risk and insurance risk

Abstract: Determining the parametric VaR approach is very important in establishing the probability distribution of a risk factor. We assume that a normal distribution is symmetric; however, it has some limitations. This distribution is used for modelling asymmetric data or data that have only positive values, such as insurance claims. The aim of the paper is to find the best probability distribution for stock exchange index returns and for insurance claims. The paper is structured as follows. Firstly, we describe the typical probability distributions used in finance, namely normal, Student, logistic, gamma, exponential and lognormal distribution, and the methods of verification. Subsequently, parameters of the distribution types are estimated via the maximum likelihood method, and after that we calculate the value at risk. The VaR is calculated even though the time series do not correspond to the stated types of probability distribution; nevertheless, we calculate the value at risk for all the stated types of probability distribution because it is apparent that large mistake can arise if an incorrect type of probability distribution is used.

Estimation of the Parameters of the Generalized Exponential Distribution in the Presence of One Outlier Generated from Uniform Distribution

Abstract: Gupta and Kundu (1999) defined the cumulative distribution function of the generalized exponential (GE). It has many properties that are quite similar to those of the gamma distribution. This paper deals with the estimation of the parameters of the generalized exponential distribution in the presence of one outlier generated from uniform distribution. The maximum likelihood, moment and mixture of the estimators are derived. These estimators are compared empirically when all of the parameters are unknown. Their bias and mean square error (MSE) are investigated with help of numerical techniques.

On Generating Distributions with the Memoryless Property

Abstract: The exponential and geometric distribution are well-known continuous and discrete family of distributions with the memoryless property, respectively. The memoryless property is emphasized in introd...