A new class of skew-logistic distribution

In this study, the researchers introduce a new class of the logistic distribution which can be used to model the unimodal data with some skewness present. The new generalization is carried out using the basic idea of Nadarajah (Statistics 48(4):872–895, 2014), called truncated-exponential skew-logistic (TESL) distribution. The TESL distribution is a member of the exponential family; therefore, the skewness parameter can be derived easier. Meanwhile, some important statistical characteristics are presented; the real data set and simulation studies are applied to evaluate the results. Also, the TESL distribution is compared to at least five other skew-logistic distributions.

Stochastic Bifurcation in Generalized Chua’s Circuit Driven by Skew-Normal Distributed Noise

In this study, the stochastic phenomenological bifurcations (P-bifurcations) of generalized Chua’s circuit (GCC) driven by skew-normal distributed noise have been investigated by numerically obtaining the stationary distributions of the stochastic responses. The noise intensity and/or skewness parameters of skew-normal distributed noise have been chosen as the bifurcation parameters to change the structure of the stochastic attractor. While the number of breakpoints in the piecewise-linear characteristics of the GCC are fixed, it has been observed that the number of scrolls have been changed by tuning the noise intensity and the skewness parameter of the skew-normal distributed noise.

Skew Generalized Secant Hyperbolic Distributions: Unconditional and Conditional Fit to Asset Returns

A generalization of the hyperbolic secant distribution which allows for both skewness and leptokurtosis was given by Morris (1982). Recently, Vaughan (2002) proposed another flexible generalization of the hyperbolic secant distribution which has a lot of nice properties but is not able to allow for skewness. For this reason, Fischer and Vaughan (2002) additionally introduced a skewness parameter by means of splitting the scale parameter and showed that most of the nice properties are preserved. We briefly reviewthis class of distributions and apply them to financial return data. By means of the Nikkei225 data, it will be shown that this class of distributions, the socalled skew generalized secant hyperbolic distribution, provides an excellent fit in the context of unconditional and conditional return models.