Approximate percentage points for Pearson distributions

Biometrika ◽  
1979 ◽  
Vol 66 (1) ◽  
pp. 147-151 ◽  
Author(s):  
K. O. BOWMAN ◽  
L. R. SHENTON
2019 ◽  
Vol 14 (1) ◽  
Author(s):  
Qing Yang ◽  
Xinming An ◽  
Wei Pan

Abstract Background Any empirical data can be approximated to one of Pearson distributions using the first four moments of the data (Elderton WP, Johnson NL. Systems of Frequency Curves. 1969; Pearson K. Philos Trans R Soc Lond Ser A. 186:343–414 1895; Solomon H, Stephens MA. J Am Stat Assoc. 73(361):153–60 1978). Thus, Pearson distributions made statistical analysis possible for data with unknown distributions. There are both extant, old-fashioned in-print tables (Pearson ES, Hartley HO. Biometrika Tables for Statisticians, vol. II. 1972) and contemporary computer programs (Amos DE, Daniel SL. Tables of percentage points of standardized pearson distributions. 1971; Bouver H, Bargmann RE. Tables of the standardized percentage points of the pearson system of curves in terms of β1 and β2. 1974; Bowman KO, Shenton LR. Biometrika. 66(1):147–51 1979; Davis CS, Stephens MA. Appl Stat. 32(3):322–7 1983; Pan W. J Stat Softw. 31(Code Snippet 2):1–6 2009) available for obtaining percentage points of Pearson distributions corresponding to certain pre-specified percentages (or probability values; e.g., 1.0%, 2.5%, 5.0%, etc.), but they are little useful in statistical analysis because we have to rely on unwieldy second difference interpolation to calculate a probability value of a Pearson distribution corresponding to a given percentage point, such as an observed test statistic in hypothesis testing. Results The present study develops a macro program to identify the appropriate type of Pearson distribution based on either input of dataset or the values of four moments and then compute and graph probability values of Pearson distributions for any given percentage points. Conclusions The SAS macro program returns accurate approximations to Pearson distributions and can efficiently facilitate researchers to conduct statistical analysis on data with unknown distributions.


2005 ◽  
pp. 4-20
Author(s):  
E. Yasin

Currency inflow in Russia from raw materials exports allows taking into account high business activity to assimilate growing money supply transforming it into economic growth. Fall in business activity as a result of pressure on business led to saturation of demand for money. This considerably increases the danger of inflation growth and requires sterilization of excess money supply including the usage of the Stabilization Fund. According to the author's estimates, corresponding losses in GDP growth will equal 1-2 percentage points per year.


TAPPI Journal ◽  
2016 ◽  
Vol 15 (7) ◽  
pp. 459-464
Author(s):  
RICARDO SANTOS ◽  
PETER HART

An automated shower water control system has been implemented to reduce the volume and variability of weak black liquor being sent from the pulp mill to the evaporators. The washing controls attempt to balance the need for consistent and low soda carryover to the bleach plant with consistently high weak black liquor solids being sent to the evaporators. The washer controls were implemented on two bleachable grade hardwood lines (one with oxygen delignification, one without oxygen delignification) and one pine line. Implementation of the control program resulted in an increase in black liquor solids of 0.6 percentage points for the hardwood lines. Significant foam reduction was realized on the pine line since the pine black liquor solids were able to be consistently maintained just below the soap separation point. Low black liquor solids excursions to the evaporators were eliminated. Bleach plant carryover was stabilized and no negative impact on chemical consumption was noticed when controlling weak black liquor solids to recovery.


Author(s):  
Bich Le Thi Ngoc

The aim of this study is to analyze empirically the impact of taxation and corruption on the growth of manufacturing firms in Vietnam. The study employed pooled OLS estimation and then instrument variables with fixed effect for the panel data of 1377 firms in Vietnam from 2005 to 2011. These data were obtained from the survey of the Central Institute for Economic Management and the Danish International Development Agency. The results show that both taxation and corruption are negatively associated with firm growth measured by firm sales adjusted according to the GDP deflator. A one-percentage point increase in the bribery rate is linked with a reduction of 16,883 percentage points in firm revenue, over four and a half times bigger than the effect of a one-percentage point increase in the tax rate. From the findings of this research, the author recommends the Vietnam government to lessen taxation on firms and that there should be an urgent revolution in anti-corruption policies as well as bureaucratic improvement in Vietnam.


2021 ◽  
Vol 7 (2) ◽  
pp. 16
Author(s):  
Pedro Furtado

Image structures are segmented automatically using deep learning (DL) for analysis and processing. The three most popular base loss functions are cross entropy (crossE), intersect-over-the-union (IoU), and dice. Which should be used, is it useful to consider simple variations, such as modifying formula coefficients? How do characteristics of different image structures influence scores? Taking three different medical image segmentation problems (segmentation of organs in magnetic resonance images (MRI), liver in computer tomography images (CT) and diabetic retinopathy lesions in eye fundus images (EFI)), we quantify loss functions and variations, as well as segmentation scores of different targets. We first describe the limitations of metrics, since loss is a metric, then we describe and test alternatives. Experimentally, we observed that DeeplabV3 outperforms UNet and fully convolutional network (FCN) in all datasets. Dice scored 1 to 6 percentage points (pp) higher than cross entropy over all datasets, IoU improved 0 to 3 pp. Varying formula coefficients improved scores, but the best choices depend on the dataset: compared to crossE, different false positive vs. false negative weights improved MRI by 12 pp, and assigning zero weight to background improved EFI by 6 pp. Multiclass segmentation scored higher than n-uniclass segmentation in MRI by 8 pp. EFI lesions score low compared to more constant structures (e.g., optic disk or even organs), but loss modifications improve those scores significantly 6 to 9 pp. Our conclusions are that dice is best, it is worth assigning 0 weight to class background and to test different weights on false positives and false negatives.


2021 ◽  
pp. 088626052110283
Author(s):  
Tyler J Lane

This study investigated whether homicides increased after protested police-involved deaths, focusing on the period after Michael Brown’s death in Ferguson in August 2014. It also tests for effects of legal cynicism by comparing effects in homicide and aggravated assault on the assumption that reporting of the latter is discretionary and police abuses may make communities reluctant to notify police. Using FBI data from 44 U.S. cities, homicide and assault rates from 2011 to 2019 were analyzed using an interrupted time series design and combined in a meta-analysis to calculate pooled effects. A meta-regression tested effect moderators including external investigations and city/county sociodemographic characteristics. With a conservative threshold of p ≤ .01, 21 of the 44 cities experienced a significant increase and one had a significant decrease. The pooled effect was a 26.1% increase in the homicide (99% CI: 15.3% to 36.8%). Aggravated assaults increased above baseline, though the effect was 15.2 percentage points smaller (99% CI: –26.7 to –3.6) than the effect in homicides. When outcomes were measured as percent change, there were no significant effect moderators, but when measured as absolute change, homicides increased to a greater extent when the death was subject to external investigation and in cities with higher Black populations, poverty rates, and baseline homicide rates. The findings suggest that protested police-involved deaths led to an increase in homicides and other violence due to the distrust fomented within the very communities whom police are meant to protect.


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