by Eugenio Brentari
by Gaetano Pietra
In Sections 2 and 3 of the present note, starting from the relations obtained in Part I between the first-order indices (mean difference, simple mean deviation, and probable deviation), some graphical representations are used in order to: 1. define the range of the aforementioned indices, by considering the features of the considered sequence of values; 2. point out the reasons for their discordance and measure the possible degree of their discordance. In Section 4 the results obtained in Part I are used, again, to study the range and the main features of the quadratic mean deviation.
by Michele M. Zenga
Keywords: Inequality, Scale Transformation Matrix, Point Inequality Index, Decomposition by Sources.
by Walid Ahmad Abu-Dayyeh, Mohammad Farah Saleh, Reyad Nammas
In this paper, we will consider the (maximum likelihood estimators) MLEs of the shape parameter p of the Weibull distribution when the scale parameter is known using (simple random sample) SRS and (ranked set sample) RSS. Some properties of these estimators will be given and a comparison between them using bias and (mean square error) MSE will be done using simulation. Also, the asymptotic distributions of the MLEs based on SRS and RSS will used to construct asymptotic confidence intervals for p. A simulation study is used to compare these confidence intervals via their expected lengths and their coverage probabilities. It appears that the MLE based on RSS can be real a competitor using SRS in all the cases considered above. A real data set is used for illustration.
Keywords: Scale Parameter, Shape Parameter, Weibull Distribution, Maximum Likelihood Estimator, Bias, Mean Square Error, Asymptotic Confidence Interval, Expected Length, Coverage Probability.
by Alessandro Fassò, Maurizio Toccu
Customers are important intangible assets of a company, but they are not equally remunerative. Therefore, to identify profitable customers, it is necessary to use a disaggregated metric called customer lifetime value (CLV). This metric represents the present value of all future profits generated by a customer. Using a known formula, it is possible to calculate customer lifetime value taking into account the survival probability of each customer. Therefore, in this paper we develop a statistical analysis of CLV using SAS. To illustrate this method we present a simple case study related to a telecommunications company. In particular, we start the study by analyzing the distribution of customers and revenues (a component of CLV) with respect to geographical area and size of customer. We continue with an analysis of the distribution of CLV with respect to the above factors, and this allows us to make a comparison, on average, with the distribution of revenues. Finally, we estimate a regression model to detect the factors affecting CLV, thereby obtaining interesting results.
Keywords: Churn Prevention, Customer Retention, Telecommunications Sector, SAS.
by Lucio De Capitani, Alessandro Zini
In this paper, the performances in fitting incomes of three different mixtures of Polisicchio distributions are compared. The considered mixtures are: the three-parameters Zenga distribution (beta mixture of Polisicchio distributions); the Generalized Zenga Distribution (confluent-hypergeometric
mixture of Polisicchio distributions) which is characterized by four parameters; and a new fiveparameters distribution defined by the Gauss-hypergeometric mixture of Polisicchio distributions. The performances of these distributions are compared in several applications showing that the behavior of the five-parameters model is substantially replicated by the more parsimonious Generalized Zenga Distribution which provides a sensible improvement in the goodness-of-fit with respect to the Zenga model when personal incomes are considered.
Keywords: Polisicchio’s Truncated Pareto Distribution, Zenga Distribution, Gaussian Hypergeometric distribution, Confluent Hypergeometric Distribution, Generalized Zenga Distribution, Incomes.