Transforming variables to central normality

Many real data sets contain numerical features (variables) whose distribution is far from normal (Gaussian). Instead, their distribution is often skewed. In order to handle such data it is customary to preprocess the variables to make them more normal. The Box–Cox and Yeo–Johnson transformations are well-known tools for this. However, the standard maximum likelihood estimator of their transformation parameter is highly sensitive to outliers, and will often try to move outliers inward at the expense of the normality of the central part of the data. We propose a modification of these transformations as well as an estimator of the transformation parameter that is robust to outliers, so the transformed data can be approximately normal in the center and a few outliers may deviate from it. It compares favorably to existing techniques in an extensive simulation study and on real data.

An Adaptive Chaotic Sine Cosine Algorithm for Constrained and Unconstrained Optimization

Sine cosine algorithm (SCA) is a new meta-heuristic approach suggested in recent years, which repeats some random steps by choosing the sine or cosine functions to find the global optimum. SCA has shown strong patterns of randomness in its searching styles. At the later stage of the algorithm, the drop of diversity of the population leads to locally oriented optimization and lazy convergence when dealing with complex problems. Therefore, this paper proposes an enriched SCA (ASCA) based on the adaptive parameters and chaotic exploitative strategy to alleviate these shortcomings. Two mechanisms are introduced into the original SCA. First, an adaptive transformation parameter is proposed to make transformation more flexible between global search and local exploitation. Then, the chaotic local search is added to augment the local searching patterns of the algorithm. The effectiveness of the ASCA is validated on a set of benchmark functions, including unimodal, multimodal, and composition functions by comparing it with several well-known and advanced meta-heuristics. Simulation results have demonstrated the significant superiority of the ASCA over other peers. Moreover, three engineering design cases are employed to study the advantage of ASCA when solving constrained optimization tasks. The experimental results have shown that the improvement of ASCA is beneficial and performs better than other methods in solving these types of problems.

A Review of Geodetic Datums of Nepal and Transformation Parameters for WGS84 to Geodetic Datum of Nepal

In Nepal there exist different coordinate systems based on different geodetic datum. The existence of these datum and coordinate systems are poorly known. In this literature the geodetic datum that is in existence in one way or other are illustrated and discussed. The next common problem encountered by users is the availability of authentic precise transformation parameter between National geodetic datum and World Geodetic Datum 1984 (WGS84) ; global datum used by global positioning system (GPS). There can exist a considerable difference in the position between local and the global system and the difference could be of several hundred meters. Based on the availability of data three sets of transformation parameters has been determined. The tests have been carried out to evaluate the accuracy of the transformation parameter in this region. The transformation parameter is recommended to transform the topographical data base of scale 1: 3500 and smaller. The accuracy of the transformation parameters are specified and can be used accordingly. This study will ultimately provide standardization and ease in transforming the coordinates from global datum (WGS84) to national geodetic datum of Nepal and vice versa.Nepalese Journal on Geoinformatics, Vol. 14, 2015, page:4-7

Limit behavior of the Esscher premium

Convergence from below of the Esscher premium for an arbitrary insurance risk to the essential supremum of the priced risk when the premium parameter tends to plus infinity is presented in the article. As a corollary of the above mentioned statement, we present convergence of the expected/averaged Esscher transform of an arbitrary random variable to its essential infimum from above when the transformation parameter tends to minus infinity.