![stata 13 skew stata 13 skew](https://www.statology.org/wp-content/uploads/2021/01/skew1.png)
Furthermore, Lin and Stoyanov established that the distribution has heavy tails and therefore it is a suitable distribution to be incorporated to the wide catalogue of heavy tails (see ). It can be seen that the parameter regulates the shape of the distribution. Observe that when expression ( 3) reduces to the classical lognormal distribution. Also, if taking and using a linear transformation, we allow for more flexible location and scale parameters in our model. Nevertheless, in this paper, we will pay special attention to the distribution arising from exponentiation of ( 2) in the following sense: if is a random variable with density ( 2),, we consider a new random variable. The basic skew lognormal distribution has been studied by Lin and Stoyanov (see also Chap. Numerical applications are provided in Section 3, and conclusions are drawn in Section 4. In Section 2, the proposed distribution is studied and some interesting properties are given. For an exhaustive and comprehensive study of the skew-normal distribution, see the recent book of Azzalini.
#Stata 13 skew pdf#
Its pdf is given byįor multivariate extensions, see for instance Azzalini and Valle, Azzalini and Capitanio, and Arnold and Beaver. In this paper, special attention is paid to the generalized skew normal density provided in Henze and also studied by Arnold and Beaver. When and are replaced in ( 1) by and, i.e., the standard normal density and distribution function, respectively, the resulting model is called the skew normal distribution. This family of distributions has been widely studied as an extension of the normal distribution via a shape parameter,, that accounts for the skewness of the model. A random variable is said to have a skew distribution if its pdf is given by Let and, respectively, be the probability density function (pdf) and the cumulative distribution function (cdf) of a symmetric distribution. These two features imply that the data cannot be adequately modelled by the Gaussian or normal distribution. This is frequently the case, for example, with actuarial and financial data that also have heavy tails reflecting the existence of extreme values. On the contrary, there exist many situations where the empirical data show slight or marked asymmetry. As an alternative to the classical Pareto distribution, other models have been recently introduced in the actuarial literature by Sarabia et al. Particularly, when calculating deductibles and excess-of-loss levels of reinsurance, the simple Pareto distribution has been proved to be convenient (see, for example, ). Concerning this, the single parameter Pareto distribution not only has nice statistical properties but also provides a good description of the random behaviour of large losses (e.g., the right tail of the distribution).
![stata 13 skew stata 13 skew](https://www.researchgate.net/profile/Kazeem-Adepoju/publication/267867948/figure/fig5/AS:295451061440514@1447452430175/Generalized-skew-t-distribution.png)
In this sense, the classical Pareto distribution has been traditionally considered as a suitable claims’ size distribution in relation to rating problems. This is an issue of particular interest in the context of reinsurance and premium calculation principles. It is our interest to find simple statistical distributions appropriate for modelling both, smaller and medium-size losses with a high frequency and large losses with a low frequency. For a comprehensive study about reinsurance, see the recent book of Albrecher et al. The modelling of large claims is a topic of relevant importance in general insurance and reinsurance, particularly in the field of mathematical risk theory, see, for instance, McNeil Beirlant and Teugels Beirlant et al. Furthermore, a regression model can be simply derived to explain the response variable as a function of a set of explanatory variables. To the best of our knowledge, this distribution has not been used in insurance context and it might be suitable for computing reinsurance premiums in situations where the right tail of the empirical distribution plays an important role. This distribution yields a satisfactory fit to empirical data in the whole range of the empirical distribution as compared to other distributions used in the actuarial statistics literature. In this paper, the three-parameter skew lognormal distribution is proposed to model actuarial data concerning losses.