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We propose two generalizations of the three-parameters Zenga distribution obtaining two families of distributions with four and five parameters. The generalizations are done starting from two different generalized beta functions and using them as mixing distributions in place of the classical beta. We compare the flexibility of the resulting models with that of the Zenga distribution observing some improvements.

The cumulative distribution and the density function of the ratio of two correlated Normal random variables has been proposed and studied by Aroian (1986) and Oksoy and Aroian (1986, 1994) and Kim (2006). For a complete review and further insights on this topic, the interested reader is referred to Galeone (2007). In Galeone and Pollastri (2012a, 2013) the quantiles of this random are used to build confidence intervals for the ratio of two means and for the incremental cost-effectiveness ratio. Pollastri and Tulli (2012) have studied the distribution of absolute ratio of two correlated Normal random variables and used it to define the confidence interval for non-negative ratio indicators. In order to ease the computation of the cumulative distribution function (cdf), the density function (df), and of the quantiles of these ratio random variables, in the present note the R-codes are presented and exemplified.

In this paper asymptotic confidence intervals for the Sortino and Omega Ratio are proposed and analyzed. First the confidence intervals are derived under the strong assumption of temporal independence and identical distribution of the returns. Later they are obtained assuming that the process followed by returns is strictly stationary and alpha-mixing of a certain size. In order to evaluate the minimum sample size for a good coverage accuracy of the asymptotic confidence intervals, a simulation study is performed. It is obtained that the minimum sample sizes are very high, especially under the more realistic assumption of not-i.i.d. returns.

In this paper, assuming that returns follows a stationary and ergodic stochastic process, the asymptotic distribution of the natural estimator of the Sharpe Ratio is explicitly given. This distribution is used in order to define an approximated confidence interval for the Sharpe ratio. Particular attention is devoted to the case of the GARCH(1,1) process. In this latter case, a simulation study is performed in order to evaluate the minimum sample size for reaching a good coverage accuracy of the asymptotic confidence intervals.

We study the estimators of three financial performance measures: the Sharpe Ratio, the Mean Difference Ratio and the Mean Absolute Deviation Ratio. The analysis is performed under two sets of assumptions. Firstly, the case of independent and identically normally distributed returns is considered. After that, relaxing the normality assumption, the case of independent and identically distributed returns is investigated. In both situations, we study the bias of the estimators and we propose their bias-corrected version. The exact and the asymptotic distribution of the three estimators is derived under the assumption of i.i.d.-normal returns. Concerning the case of i.i.d. returns, the asymptotic distributions of the estimators are provided. The latter distributions are used to define exact or large sample confidence intervals for the three indices. Finally, we perform a simulation study in order to assess the efficiency of the bias corrected estimator, the coverage accuracy and the length of the asymptotic confidence intervals

The need of an ethical evaluation is mandatory for every clinical trial, Ethics Committees have been built for that. The distinction between individual and collective ethics has been introduced in a seminal work by Lellouch and Schwartz in 1971, where individual ethics regard concerns related to the patients enrolled in the trial, and collective ethics those of the patients not enrolled who would benefit of a positive trial result. In this paper, a metrization of individual and collective ethics is proposed in order to evaluate their balance in a confirmatory clinical trial. The ethical balance evaluation, among these two aspects of ethics, can be performed before trial starting in order to address sample size determination. The metrization is based, among other parameters, on the drug effect size, on the quality of life of patients under therapy or placebo, and of that induced by adverse reactions. Some numerical examples show that the optimal ethical balance can be provided by sample sizes far from those computed by adopting the usual paradigm based on the prefixed power of 80-90%

In thiswork,Bivariate Burr-III copula is extended to the trivariate case. This copula seems to be very general and analytically manageable and it provides an alternative to the commonly employed elliptical copulas (such as the Gaussian or the Stutent’s t ones) since they have, roughly, the same number of parameters. Several applications to income and wine data are described in the paper. They show that the Trivariate Burr-III copula is, in general, able to capture the dependence structure implicit in observed trivariate data. Moreover, they show that the third-order interaction parameter results, in some cases, significant at 1% significance level while, in other cases, it can be removed from the fitted model. The ability of the Trivariate Burr-III copula in representing the dependence structure implicit in the considered data is compared with the ones of other well known copulas: the Clayton copula, the t copula, and the Skew-t copula. It results that the Trivariate Burr-III copula provides a good fitting and turns out to be the best performer in fitting the considered wine data but, on income data, the best performers are the t and Skew-t copulas. The over-performance of the last two copulas on income data is probably due to their ability in representing right-tail dependence (a kind of dependence that is not taken into account by the Trivariate Burr-III copula)

In this work we compare nonparametric estimators for finite population distribution functions based on two types of fitted values: the fitted values from the well-known Kuo estimator and a modified version of them, which incorporates a nonparametric estimate for the mean regression function. For each type of fitted values we consider the corresponding model-based estimator and, after incorporating design weights, the corresponding generalized difference estimator. We show under fairly general conditions that the leading term in the model mean square error is not affected by the modification of the fitted values, even though it slows down the convergence rate for the model bias. Second order terms of the model mean square errors are difficult to obtain and will not be derived in the present paper. It remains thus an open question whether the modified fitted values bring about some benefit from the model-based perspective. We discuss also design-based properties of the estimators and propose a variance estimator for the generalized difference estimator based on the modified fitted values. Finally, we perform a simulation study. The simulation results suggest that the modified fitted values lead to a considerable reduction of the design mean square error if the sample size is small.

Detecting and measuring lag-dependencies is very important in time-series analysis. This study is commonly carried out by focusing on the linear lag-dependencies via the well-known autocorrelogram. However, in practice, there are many situations in which the autocorrelogram fails because of the nonlinear structure of the serial dependence. To cope with this problem, in this paper the R package SDD is introduced. Among the available approaches to analyze the lag-dependencies in an omnibus way, the SDD package considers the autodependogram and some of its variants. The autodependogram, defined by computing the classical Pearson ­2-statistic at various lags, is a graphical device recently proposed in the literature to analyze lag-dependencies. The concept of reproducibility probability, and several density-based measures of divergence, are considered to de ne the variants of the autodependogram. An application to daily returns of the Swiss Market Index is also presented to exemplify the use of the package.

In this work the precision of point and interval estimators for some performance measures for risky financial assets is analyzed and the conditions under which the point estimators are asymptotically normally distributed are provided. The findings of this research suggest that a huge number of observations is needed to get reasonably precise point and interval estimates. Therefore, the considered performance measures may be surely employed as descriptive statistics for ex-post performance comparisons but they should be employed with caution in ex-ante evaluations for investment choices.

Detecting and measuring lag-dependencies is very important in time-series analysis. This study is commonly carried out by focusing on the linear lag-dependencies via the well-known autocorrelogram. However, in practice, there are many situations in which the autocorrelogram fails because of the nonlinear structure of the serial dependence. To cope with this problem, in this paper the R package SDD is introduced. Among the available approaches to analyze the lag-dependencies in an omnibus way, the SDD package considers the autodependogram and some its variants. The autodependogram, de ned computing the classical Pearson chi-square statistics of independence at various lags, is a graphical device recently proposed in the literature to analyze lag-dependencies. The concept of reproducibility probability, and several density-based measures of divergence, are considered to de ne the variants of the autodependogram. An application to daily returns of the Swiss Market Index is also presented to exemplify the use of the package.

In this work we propose a new estimator for the finite population distribution function of a study variable that uses knowledge about an auxiliary variable. The new estimator is based on a nonparametric superpopulation model that allows for nonlinear regression functions and not identically distributed error components. It employs two local linear regressions to estimate first the regression function and then the cdf of the error components. We propose two versions of the new estimator: a model-based version and a model-assisted one. Their performance is compared with that of several well-known estimators in a simulation study under simple random without replacement sampling and under Poisson sampling with nonconstant inclusion probabilities. The simulation results show that both versions of the new estimator perform very steadily in a great variety of populations and that they are particularly efficient in populations that are best fitted by a nonlinear regression function with regression residuals that do not follow a definite pattern.

In this work we compare finite population quantile estimators in a simulation study. We consider settings where complete auxiliary information is available, and quantile estimators that are obtained from inversion of several well-known estimators for the population cdf. The simulation results show that estimators based on separate estimates of the regression function and the error distributions are usually the most efficient ones.

This article reviews some nonparametric serial independence tests based on measures of divergence between densities. Among others, the well-known Kullback-Leibler, Hellinger, Tsallis, and Rosenblatt divergences are analyzed. Moreover, their copula-based version is taken into account. Via a wide simulation study, the performances of the considered serial independence tests are compared under different settings. Both single-lag and multiple-lag testing procedures are investigated to find out the best "omnibus" solution.

The autodependogram is a graphical device recently proposed in the literature to analyze autodependencies. This paper proposes a normalization of this diagram taking into consideration the concept of reproducibility probability (RP). The result is a novel tool, named RP-autodependogram, which permits to study the strength and the stability of the evidence about the presence of lag-dependence. A simulation study on well-established time-series models is carried out to investigate the behavior of the RP-autodependogram also in comparison with other diagrams studying autodependencies. An application to financial data is finally considered to appreciate its usefulness in the identification of parametric/nonparametric models. © 2013 Springer-Verlag Berlin Heidelberg.

In this work we propose a new estimator for the finite population cdf of a study variable that combines the two approaches to exploit knowledge about an auxiliary variable used in the Chambers and Dunstan ([2]) and the Kuo ([5]) estimators. As both the latter estimators, the new estimator is based on a superpopulation model where the population values of the study variable are generated independently from a model-cdf that is allowed to depend smoothly on an auxiliary variable. Like the Chambers and Dunstan estimator, the new estimator is based on estimates for the model-cdf of the study variable that are obtained by estimating the model-mean regression function and the model-cdf of the error terms separately. In the new estimator however both estimation steps are performed by non parametric regression in order to account for superpopulation models with smooth mean regression function and error term distribution that depends smoothly on the auxiliary variable. The non parametric regression for estimating model-cdf of the error terms resembles the one used in the Kuo estimator to estimate the model-cdf of the study variable directly, without considering the model-mean regression function. We will present a simulation study which shows that the new estimator outperforms several well known estimators from literature when the error terms are independently but not identically distributed.

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 five-parameters 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.

We propose a generalization of the three-parameters Zenga distribution obtaining a four-parameters model. The generalization is performed using the confluent hypergeometric distribution as mixing distributions in place of the classical beta. We compare the flexibility of the resulting model with that of the Zenga distribution observing some improvements.

In this paper, assuming that returns follows a stationary and ergodic stochastic process, the asymptotic distribution of the natural estimator of the Sharpe Ratio is explicitly given. This distribution is used in order to define an approximated confidence interval for the Sharpe ratio. Particular attention is devoted to the case of the GARCH(1,1) process. In this latter case, a simulation study is performed in order to evaluate the minimum sample size for reaching a good coverage accuracy of the asymptotic confidence intervals

This article reviews the nonparametric serial independence tests based on measures of divergence between densities. Among others, the well-known Kullback-Leibler, Hellinger and Tsallis divergences are analyzed.Moreover, the copulabased version of the considered divergence functionals is defined and taken into account. In order to implement serial independence tests based on these divergence functionals, it is necessary to choose a density estimation technique, a way to compute p-values and other settings. Via a wide simulation study, the performance of the serial independence tests arising from the adoption of the divergence functionals with different implementation is compared. Both single-lag and multiple-lag test procedures are investigated in order to find the best solutions in terms of size and power.

We study the estimators of three financial performance measures: the Sharpe Ratio, the Mean Difference Ratio and the Mean Absolute Deviation Ratio. The analysis is performed under two sets of assumptions. First, the case of i.i.d. Normal returns is considered. After that, relaxing the normality assumption, the case of i.i.d. returns is investigated. In both situations, we study the bias of the estimators and we propose their bias-corrected version. The exact and asymptotic distribution of the three estimators is derived under the assumption of i.i.d. Normal returns. Concerning the case of i.i.d. returns, the asymptotic distribution of the estimators is provided. The latter distributions are used to define exact or asymptotic confidence intervals for the three indices. Finally, we perform a simulation study in order to assess the efficiency of the bias corrected estimators, the coverage accuracy and the length of the asymptotic confidence intervals.

Recently, the possibility of testing statistical hypotheses through the estimate of the reproducibility probability (i.e. the estimate of the power of the statistical test) in a general parametric framework has been introduced. In this paper, we provide some results on the stochastic orderings of the Wilcoxon Rank Sum (WRS) statistic, implying, for example, that the related test is strictly unbiased. Moreover, under some regularity conditions, we show that it is possible to define a continuous and strictly monotone power function of the WRS test. This last result is useful in order to obtain a point estimator and lower bounds for the power of the WRS test. In analogy with the parametric setting, we show that these power estimators, alias reproducibility probability estimators, can be used as test statistic, i.e. it is possible to refer directly to the estimate of the reproducibility probability to perform the WRS test. Some reproducibility probability estimators based on asymptotic approximations of the power are provided. A brief simulation shows a very high agreement between the approximated reproducibility probability based tests and the classical one. © 2011 Elsevier B.V.