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digital STATISTICA & APPLICAZIONI - 2011 - 2
Digital issue
issue 3 - 2011
publisher Vita e Pensiero
format Digital issue | Pdf
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Chi-Square goodness of fit test for logistic distribution using RSS and SRS
by Mohd T. Alodat, Kamarulzaman Ibrahim, Abdul A. Jemain, Sameer A. Al-Subh pages: 18 Download
In this paper, we introduce a new method to improve the power of the chi-square test for goodness of fit (GOF) of logistic distribution under selective order ranked Set sampling (RSS) based on minimum, median and maximum as compared to simple random sampling (SRS). Based on a simulation study, we illustrate that the chi-square test is found to be more powerful under selective order RSS when compared to SRS, particularly for minimum and maximum. However, for the case of median RSS, the test is found to be more powerful under SRS. To investigate these results further, the Kullback- Leibler information (KLI) is applied and similar results are found.

Keywords: Goodness of fit test, chi-square test, logistic distribution, ranked set sample, simple random sample.
Point and interval estimation for some financial performance measures
by Michele Zenga, Lucio De Capitani pages: 30 Download
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.

Keywords: Financial Performance Measure, Sharpe Ratio, Mean Difference Ratio, Mean Absolute Deviation Ratio, Concentration Measures, Statistical Analysis of Financial Data.
Improved group acceptance sampling plans for the gamma distributed items
by Muhammad Aslam, Maryam Fatima, Ahmed Bani-Mustafa, Amjad D. Al-Nasser pages: 15 Download
In this paper, a time truncated group acceptance sampling plan (GASP) is designed under the Gamma distribution. The present plan is modification of the existing plan to reduce the number of groups/sample size. The plan parameters are obtained by satisfying the producer’s risk and consumer’s risk (two points approach) for specified values of mean ratio and number of testers. The single point approach is also used to find plan parameters such as number of groups for specified values of acceptance number and experiment time. The extensive tables, graphs and examples are given for illustration purposes. The advantage of the proposed plan discussed over the existing plans.

Keywords: Group Acceptance Sampling; Consumer’s Risk; Producer’s Risk; Gamma Distribution; Operating Characteristic Values.
The Confidence Ellipses in Multiple Non-Symmetrical Correspondence Analysis for the Evaluation of the Innovative Performance of the manufacturing enterprises in Campania
by Anna Crisci, Antonello D'Ambra pages: 13 Download
Non-Symmetric Correspondence Analysis-NSCA (D’Ambra and Lauro, 1989) is a useful technique for analyzing a two-way contingency table. There are many real-life applications where it is not appropriate to perform classical correspondence analysis because of the obvious asymmetry of the association between the variables. The key difference between the symmetrical and non-symmetrical versions of correspondence analysis rests on the measure of the association used to quantify the relationship between the variables. For a two-way, or multi-way, contingency table, the Pearson chisquared statistic is commonly used when it can be assumed that the categorical variables are symmetrically related. However, for a two-way table, it may be that one variable can be treated as a predictor variable and the second variable can be considered as a response variable. Yet, for such a variable structure, the Pearson chi-squared statistic is not an appropriate measure of the association. Instead, one may consider the Goodman-Kruskal tau index. In the case that there are more than two cross-classified variables, multivariate versions of the Goodman-Kruskal tau index can be considered. These include Marcotorchino’s index (Marcotorchino, 1985) and Gray-Williams’ index (Gray and Williams, 1975). In the present paper, the Multiple non- Symmetric Correspondence Analysis- MNSCA (Gray and Williams, J. S,1975), is used for the evaluation of the innovative performance of the manufacturing enterprises in Campania. Innovation represents a very important element for the competition of the enterprises and economic growth. Only the enterprises which are able to innovate regularly can have at their disposal a range of more and more appealing products for the customers. Moreover, only a constant innovation provides the constant efficiency of the processes and the optimization of the production costs. Finally, the use of the ellipse confidence has allowed to identify a category which is statistically significant.

Keywords: CATANOVA, Confidence Ellipse, Gray-Williams Multiple Tau Index, Multiple Non Symmetrical Correspondence Analysis
The effect of education and ability. An estimation on the labour income of Italian graduates
by Antonino Di Pino, Patrizia Pulejo pages: 18 Download
In this paper we present a method for estimating the effect of college education independent of individual ability. We use a matching procedure to compare graduates and high school diploma holders (the latter to be used as counterfactuals) in order to identify both treatment and ability parameters in a two-regime equation model. A sensitivity analysis suggests that our matching results are robust with respect to a possible bias due to unobserved heterogeneity. Using Istat’s Survey on Italian Graduates, we estimate that the average effect of one year of college attendance on labour income is close to 7.5%. Unlike the results reported in recent literature, the effect of education is not higher for better endowed individuals.

Keywords: Ability Bias, Matching, Treatment Effects Estimation, Two-Regime Regression Model.
Perception of poverty. Individual, household and social enviromental determinants
by Isabella Santini pages: 17 Download
This paper aims to show to what extent self-perception of poverty is affected by respondent/household socio-economic characteristics and by social capital endowment of household place of residence in order to disclose the primary risk factors of family poverty status. Such evidence would help central and local government to define those economic and social goals which should receive more attention by current policies with the purpose of advancing towards the eradication of poverty. In order to purse this aim the logit model has been applied to analyze answers to the dichotomous transformation of the following question taken from the 2008 Survey on Household Income and Wealth (SHIW) of the Bank of Italy CONSIDERING YOUR MONTHLY DISPOSABLE INCOME, IS YOUR HOUSEHOLD ABLE TO MAKE ENDS MEET: (1) WITH GREAT DIFFICULTY, (2) WITH DIFFICULTY, (3) WITH SOME DIFFICULTY, (4) WITHOUT DIFFICULTY, (5) WITH EASE, (6) WITH GREAT EASE? The results show a relevant effect on self-perception of poverty of both respondent /household socio-economic characteristics and social capital. In particular, the components social relationships and social engagement contribute to reduce the risk of a self-perceived poverty. Actually, networks characterized by relationships of trust are key determinants of human welfare as people socio-economic vulnerability is reduced as well as the resources they need only for the fact that they must deal with risk and avert major losses.

Keywords: Self-perception of Poverty, Social Capital, Household Socio-Economic Characteristics, Policy-Makers