This paper rigorously demonstrates that for any unequal income distribution, the well-known Gini index of inequality is bounded above by recently revived Bonferroni index. The bound exactly attained if and only out n incomes in society, − 1 poor are identical. boundedness theorem shown to possess a duality-type implication. These two metrics, popular members general class indices generated Aabe...

One of the simplest and most widely used multiple comparison tests is the Bonferroni adjustment (test). It is applicable to the following situations: 1) Regardless of whether or not the sample sizes of each group are equal. 2) When the family of interest is the particular set of comparisons (not all pair-wise comparisons). We can easily obtain the results of the Bonferroni comparison by multipl...

Methods All mechanically ventilated patients staying >72h in ICU, with Fi02 < 60%, PEEP < 9cmH2O, no pulmonary fistula or lung multi-resistant bacteria were included and had IC measurement. We calculated EE with the ESPEN equation (20-25 kcal/kg acute phase and 25-30 kcal/kg post-acute phase), using several BW: anamnestic (BWAN), measured (BWMES), adjusted for water balance (BWADJ) and ideal BW...

Methods: Resin-modified glass ionomer (Vitremer – V), microhybrid composite resin with fluoride (Tetric Ceram – T), and nanofiller composite resin without fluoride (Z350 – Z) were evaluated. Acidulated phosphate fluoride (APF, 1.23%) was applied to half of the specimens (groups VF, TF, ZF and EF). Ten intact human third molars were used to obtain enamel specimens (E). Six experimental groups (n...

Hochberg & Benjamini (1990) first presented adaptive procedures for controlling familywise error rate. However, until now, it has not been proved that these procedures control the familywise error rate. We introduce a simplified version of Hochberg & Benjamini’s adaptive Bonferroni and Holm procedures. Assuming a conditional dependence model, we prove that the former procedure controls the fami...

Let A1, A2, . . . , Am and B1, B2, . . . , Bn be two sequences of events on the same probability space. Let X = Xm(A) and Y = Yn(B), respectively, denote the numbers of those Ai’s and Bj ’s which occur. We establish new bivariate Bonferroni-type inequalities using consecutive events and deduce a known result.

This article addresses the various mathematical and statistical properties of Burr type XII distribution (such as quantiles, moments, moment generating function, hazard rate, conditional mean residual lifetime, past deviation about median, stochasic ordering, stress-strength parameter, entropies, Bonferroni Lorenz curves order statistics) are derived. We discuss some exact expressions recurrenc...