Vita e Pensiero

A new three-parameter density function f ðx :
; ; Þ for non-negative variables, obtained as a mixture of ‘‘Polisicchio’s truncated Pareto distributions’’, is proposed. The expectation of f ðx :
; ; Þ is equal to the parameter
> 0. The new density has positive asymmetry and Paretian right tail. The variance is equal to
2 3 ð þ 1Þ ½2 þ ð
1Þ
 . The moments, the upper and lower truncated moments (with truncation at x ¼
), are compact expressions of beta functions. Keywords: Income Distribution, Positive Asymmetry, Paretian Tail, Mixture Density, Beta Weights

In this paper two tests of serial independence are proposed. The building block of these procedures is the definition of a component
2-test for testing independence between pairs of lagged variables. With reference to different component
2-tests, it is shown that the corresponding test statistics are independent. Taking advantage of this result, the component tests are used from both a simultaneous and a direct viewpoint to define two different test procedures denoted by SIS (Serial Independence Simultaneous) and SICS (Serial Independence Chi-Square). Simulations are used to explore the performance of these tests in terms of size and power. Our results underline that both the proposals are powerful against various types of alternatives. It is also shown, through what we call Lag Subsets Dependence Plot (LSDP), how to detect possible lag(s)-dependences graphically. Some examples are finally provided in order to evaluate the effectiveness of the LSDP. Keywords: Nonlinear Time Series, Serial Independence, Simultaneous Tests,
2-test.

In this paper, we consider the problem of constructing confidence intervals for the normal population mean when the coefficient of variation is known. We obtain 13 confidence intervals using different pivots. Also we conduct a simulation study to compare the expectations as well as the standard deviations of the intervals lengths. Keywords: Coefficient of Variation, Normal Distribution, Pivotal Method, Confidence Interval.

In this paper we derive nonparametric Bayesian estimate for a real parameter of a measure which is, in its turn, the function parameter of a mixture of a Dirichlet process and credibility interval for the predictive value. We apply this approach to data of plant species of relative abundance as given by Alodat, Odat, Muhaidat and Beldjillali (2008). Keywords: Power Function Distribution, Bayes Estimator, Prior Distribution, Plant Relatives abundance.

The body of econometric estimation theory in linear models must necessarily hinge, as a frame of reference, on Rao’s unified theories of linear estimation and least squares. The mathematical counterpart of the basic statistical setups turns out to be quadratic optimization problems, whose solutions yield the optimal estimators. These solutions rest on the inversion of the fundamental bordered matrix of the first-order conditions for optimality. A recently devised partitioned inversion rule leads to a mother formula for estimators within a linear framework. In addition, this paper casts further light on the link between the best fit approach to estimation and model specifications. Indeed, by taking least squares as a bridge-head and best unbiasedness as a benchmark, quite a deep insight into parameter inference is gained, whose applicative spin-offs are brought to light by a wide-ranging reappraisal of statistic and econometric estimators. Keywords: Least squares, Econometric models, Best unbiasedness, Orthogonal complements,Inversion rules. L’econometria metodologica ha nelle teorie unificate della stima lineare e dei minimi quadrati di Rao i suoi riscontri naturali. Ai sensi di tali teorie, il problema di stima si riconduce ad un problema di ottimizzazione matematica che trova nell’inversione della cosiddetta ‘‘matrice orlata fondamentale’’ la chiave per la sua soluzione. Una recente formula di inversione per parti consente di pervenire ad una formula madre per la classe degli stimatori ottimali nei modelli lineari. Da questa analisi emergono altresı`interessanti collegamenti col problema del modello di riferimento, per un dato metodo di stima di accostamento ottimale, e dualmente col problema dei minimi quadrati che conduce allo stimatore ottimale per una data specificazione lineare. L’articolo fornisce un contributo chiarificatore, con apporti innovativi, a questi temi di preminente interesse per l’econometria nelle sue interazioni con la statistica.

The moving extreme ranked set sampling, introduced by Alodat and Al-Saleh (2001), is a modification of the well known ranked set sampling approach that was proposed by McIntyre (1952). In this paper, we suggest new estimators for the simple linear regression parameters under the moving extreme ranked set sampling scheme. Moreover, we show that the proposed estimators are more efficient than their counterparts using the simple random sampling approach. We illustrate our ideas and thoughts via simulation and data analysis and conduct a comparison between our approach and the traditional ones. Keywords: Moving ranked set sampling, Ranked set sampling, Simple linear regression.