Fast Clustering Environment Impact using Multi Soft Set Based on Multivariate Distribution

Every development activity is always related to human or community aspects. This can also lead to changes in the characteristics of the community. The community's increasing awareness and critical attitude need to be accommodated to avoid the emergence of social conflicts in the future. This research is to find out how the public perception about the impact of development on the environment. Two methods are used, i.e., MDA (Maximum Dependency Attribute) and MSMD (the Multi soft set multivariate distribution function). The MDA is to determine the most influential attribute and the Multi soft set multivariate distribution function (MSMD) is to group the selected data into classes with similar characteristics. This will help the police producer plan the right mediation and take quick activity to make strides in the quality of the social environment. The experiment conducted level of impact based on the clustering results with the greatest number of member clusters is cluster 1 (very low impact) with 32.25 % of total data following cluster 5 (Very High impact) with 24.25 % of total data. The experiment obtains the level of impact based on the clustering results. The greatest number of member clusters is cluster 1 (extremely low impact) with 32.25 % of total data following cluster 5 (Very High impact) with 24.25 % of total data. The scatter area impact is spread at districts 6, 7, 10, 11, the most of very high impact and districts 1,2,3,4,5,8 the lowest impact.

On the Lifetime and Signature of Constrained (k, d)-out-of-n: F Reliability Systems

In the present paper we carry out a reliability study of the constrained (k, d)-out-of-n: F systems with exchangeable components. The signature vector is computed by the aid of the proposed algorithm. In addition, explicit signature-based expressions for the corresponding mean residual lifetime and the conditional mean residual lifetime of the aforementioned reliability system are also provided. For illustration purposes, a well-known multivariate distribution for modelling the lifetimes of the components of the constrained (k, d)-out-of-n: F structure is considered.

Constructing a multivariate distribution function with a vine copula: towards multivariate luminosity and mass functions

ABSTRACT The need for a method to construct multidimensional distribution function is increasing recently, in the era of huge multiwavelength surveys. We have proposed a systematic method to build a bivariate luminosity or mass function of galaxies by using a copula. It allows us to construct a distribution function when only its marginal distributions are known, and we have to estimate the dependence structure from data. A typical example is the situation that we have univariate luminosity functions at some wavelengths for a survey, but the joint distribution is unknown. Main limitation of the copula method is that it is not easy to extend a joint function to higher dimensions (d > 2), except some special cases like multidimensional Gaussian. Even if we find such a multivariate analytic function in some fortunate case, it would often be inflexible and impractical. In this work, we show a systematic method to extend the copula method to unlimitedly higher dimensions by a vine copula. This is based on the pair-copula decomposition of a general multivariate distribution. We show how the vine copula construction is flexible and extendable. We also present an example of the construction of a stellar mass–atomic gas–molecular gas three-dimensional mass function. We demonstrate the maximum likelihood estimation of the best functional form for this function, as well as a proper model selection via vine copula.

Differentially Private Release of Datasets using Gaussian Copula

We propose a generic mechanism to efficiently release differentially private synthetic versions of high-dimensional datasets with high utility. The core technique in our mechanism is the use of copulas, which are functions representing dependencies among random variables with a multivariate distribution. Specifically, we use the Gaussian copula to define dependencies of attributes in the input dataset, whose rows are modelled as samples from an unknown multivariate distribution, and then sample synthetic records through this copula. Despite the inherently numerical nature of Gaussian correlations we construct a method that is applicable to both numerical and categorical attributes alike. Our mechanism is efficient in that it only takes time proportional to the square of the number of attributes in the dataset. We propose a differentially private way of constructing the Gaussian copula without compromising computational efficiency. Through experiments on three real-world datasets, we show that we can obtain highly accurate answers to the set of all one-way marginal, and two-and three-way positive conjunction queries, with 99% of the query answers having absolute (fractional) error rates between 0.01 to 3%. Furthermore, for a majority of two-way and three-way queries, we outperform independent noise addition through the well-known Laplace mechanism. In terms of computational time we demonstrate that our mechanism can output synthetic datasets in around 6 minutes 47 seconds on average with an input dataset of about 200 binary attributes and more than 32,000 rows, and about 2 hours 30 mins to execute a much larger dataset of about 700 binary attributes and more than 5 million rows. To further demonstrate scalability, we ran the mechanism on larger (artificial) datasets with 1,000 and 2,000 binary attributes (and 5 million rows) obtaining synthetic outputs in approximately 6 and 19 hours, respectively. These are highly feasible times for synthetic datasets, which are one-off releases.

ONE-YEAR PREMIUM RISK AND EMERGENCE PATTERN OF ULTIMATE LOSS BASED ON CONDITIONAL DISTRIBUTION

We study the relation between one-year premium risk and ultimate premium risk. In practice, the one-year risk is sometimes related to the ultimate risk by using a so-called emergence pattern formula which postulates a linear relation between both risks. We define the true emergence pattern of the ultimate loss for the one-year premium risk based on a conditional distribution of the ultimate loss derived from a multivariate distribution of the claims development process. We investigate three models commonly used in claims reserving and prove that the true emergence pattern formulas are different from the linear emergence pattern formula used in practice. We show that the one-year risk, when measured by VaR, can be under and overestimated if the linear emergence pattern formula is applied. We present two modifications of the linear emergence pattern formula. These modifications allow us to go beyond the claims development models investigated in the first part and work with an arbitrary distribution of the ultimate loss.