scholarly journals Computing and graphing probability values of pearson distributions: a SAS/IML macro

2019 ◽  
Vol 14 (1) ◽  
Author(s):  
Qing Yang ◽  
Xinming An ◽  
Wei Pan
Keyword(s):  
Statistical Analysis ◽  
Test Statistic ◽  
Stat Assoc ◽  
Pearson Distribution ◽  
Pearson System ◽  
Percentage Points ◽  
Sas Macro ◽  
Pearson Distributions ◽  
First Four Moments ◽  
Frequency Curves

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.

Was This in Your Statistics Textbook? IV. Frequency Data

1989 ◽  
Vol 25 (1) ◽  
pp. 11-25
Author(s):  
D. J. Finney
Keyword(s):  
Statistical Analysis ◽  
Contingency Tables ◽  
The Other ◽  
Frequency Data ◽  
Significance Tests ◽  
Test Statistic ◽  
Jumping To Conclusions ◽  
Proper Role ◽  
Measure Of Association

SUMMARYObservations that are frequencies rather than measurements often call for special types of statistical analysis. This paper comments on circumstances in which methods for one type of data can sensibly be used for the other. A section on two-way contingency tables emphasizes the proper role of χ2 a test statistic but not a measure of association; it mentions the distinction between one-tail and two-tail significance tests and reminds the reader of dangers. Multiway tables bring new complications, and the problems of interactions when additional classificatory factors are explicit or hidden are discussed at some length. A brief outline attempts to show how probit, logit, and similar techniques are related to the analysis of contingency tables. Finally, three unusual examples are described as illustrations of the care that is needed to avoid jumping to conclusions on how frequency data should be analysed.

scholarly journals PENGARUH LATIHAN TERPUSAT DAN LATIHAN ACAK TERHADAP HASIL PENGUASAAN TEKNIK DASAR BOLA BASKET

KINESTETIK ◽  
2018 ◽  
Vol 2 (1) ◽  
pp. 36-43
Author(s):  
Setiana Wati ◽  
Tono Sugihartono ◽  
Sugiyanto Sugiyanto
Keyword(s):  
Statistical Analysis ◽  
Experimental Methods ◽  
Statistical Test ◽  
T Test ◽  
Distributed Data ◽  
Statistical Calculation ◽  
Test Statistic ◽  
Basic Technique ◽  
Test Criterion ◽  
Experimental Group

Abstrak Penelitian ini bertujuan untuk mengetahui pengaruh antara latihan terpusat dan latihan acak terhadap hasil penguasaan teknik dasar bola basket. Penelitian ini menggunakan metode eksperimen yang dilakukan terhadap dua kelompok, yaitu kelompok eksperimen satu yang di beri perlakuan latihan terpusat dan kelompok eksperimen dua di beri perlakuan latihan acak. Penelitian dilakukan di Klub Basket Poltekkes Kemenkes Bengkulu dengan sampel yang di pilih berdasarkan karakteristik tertentu. Analisis statistik yang di gunakan dalam penelitian ini adalah Uji t untuk menguji hipotesis bahwa “latihan acak memberikan pengaruh lebih baik dibandingkan dengan latihan terpusat dalam meningkatkan keterampilan teknik dasar bola basket”. Uji syarat statistik t telah memenuhi syarat homogen dan data berdistribusi normal berdasarkan perhitungan statistik dan pengujian kriteria uji statistic di dapat hasil bahwa latihan terpusat dan latihan acak memberikan pengaruh terhadap hasil penguasaan teknik dasar bola basket. Hal ini diketahui dari data thitung = -5,11 > ttabel = 2,11 dengan taraf ?=0,05. Kesimpulan dari penelitian ini dilihat dari hasil uji signifikan perbedaan peningkatan latihan kedua kelompok menunjukkan bahwa latihan acak memberikan pengaruh yang lebih signifikan terhadap hasil  penguasaan teknik dasar bola basket. Kata Kunci: Latihan terpusat, Latihan acak, Teknik Dasar Bola Basket.Abstract This study aims to determine the effect of centralized training and random exercise on the results of mastery of basic techniques of basketball. This study used experimental methods conducted on two groups, namely the experimental group one which was given the treatment of centralized exercise and the experimental group of two in the treatment of random treatment. The research was conducted at Club Basket Poltekkes Kemenkes Bengkulu with selected samples based on certain characteristics. The statistical analysis used in this study is t-test to test the hypothesis that "randomized exercise gives better effect than centralized training in improving basic basketball technique skills". Test statistic requirement t has complied with homogeneous requirements and normal distributed data based on statistical calculation and statistical test criterion test in can result that centralized exercise and random exercise have an effect on the result of mastery of basic technique of basketball. It is known from thitung = -5,11> ttable = 2,11 with ? = 0,05. The conclusions of this study seen from the results of significant test differences in the improvement of the two groups showed that the random exercise gives a more significant effect on the results of mastery of basic techniques of basketball. Keywords: Centralized exercise, Random exercise, Basic Basketball Technique.

scholarly journals Precipitation Regime and Temporal Changes in the Central Danubian Lowland Region

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Dana Halmova ◽  
Pavla Pekarova ◽  
Juraj Olbrimek ◽  
Pavol Miklanek ◽  
Jan Pekar
Keyword(s):  
Spectral Analysis ◽  
Statistical Analysis ◽  
Daily Precipitation ◽  
Point Of View ◽  
Annual Precipitation ◽  
Annual Maximum ◽  
Precipitation Regime ◽  
Initial Hypothesis ◽  
Frequency Curves

The aim of this paper is to investigate the statistical aspects of multiannual variability of precipitation at the Hurbanovo station, Slovakia, over 140 years (1872–2011). We compare the long-term variability of annual precipitation for Hurbanovo (Slovakia), Brno (Czech Republic), Vienna (Austria), and Mosonmagyarovar (Hungary) stations using autocorrelation and spectral analysis methods. From the long-term point of view, there is no consistent trend in the annual precipitation; only a multiannual variability has been detected. Consequently we identify changes in the distribution of annual maximum daily precipitation for Hurbanovo during different periods for winter-spring and summer-autumn seasons using histograms, empirical exceedance curves, and frequency curves of daily precipitation. Next, we calculate the periods of days without precipitation exceeding 29 days between 1872 and 2011. The longest period of days without precipitation was 83 days in 1947. The statistical analysis does not confirm our initial hypothesis that neither high daily precipitation (over 51.2 mm per day) nor long dry periods (more than 50 days without precipitation) would occur more frequently nowadays. We assume that the decrease in annual precipitation over the period 1942–2011 (compared to 1872–1941) is caused by the less frequent occurrence of daily precipitation between 0.4 and 25.6 mm.

scholarly journals Robust Nonparametric Methods of Statistical Analysis of Wind Velocity Components in Acoustic Sounding of the Lower Layer of the Atmosphere

Symmetry ◽  
2019 ◽  
Vol 11 (8) ◽  
pp. 961 ◽  
Author(s):  
Krasnenko ◽  
Simakhin ◽  
Shamanaeva ◽  
Cherepanov
Keyword(s):  
Statistical Analysis ◽  
Wind Velocity ◽  
Numerical Experiments ◽  
Lower Layer ◽  
Statistical Characteristics ◽  
Nonparametric Method ◽  
Vertical Profiles ◽  
Acoustic Sounding ◽  
Sodar Data ◽  
First Four Moments

Statistical analysis of the results of minisodar measurements of vertical profiles of wind velocity components in a 5–200 m layer of the atmosphere shows that this problem belongs to the class of robust nonparametric problems of mathematical statistics. In this work, a new consecutive nonparametric method of adaptive pendular truncation is suggested for outlier detection and selection in sodar data. The method is implemented in a censoring algorithm. The efficiency of the suggested algorithm is tested in numerical experiments. The algorithm has been used to calculate statistical characteristics of wind velocity components, including vertical profiles of the first four moments, the correlation coefficient, and the autocorrelation and structure functions of wind velocity components. The results obtained are compared with classical sample estimates.

scholarly journals Goodness of Fit Tests for Marshal-Olkin Extended Rayleigh Distribution

2019 ◽  
pp. 587-598
Author(s):  
Naz Saud ◽  
Sohail Chand
Keyword(s):  
Goodness Of Fit ◽  
Empirical Distribution ◽  
Rayleigh Distribution ◽  
Test Statistic ◽  
Goodness Of Fit Test ◽  
Goodness Of Fit Tests ◽  
Estimated Parameters ◽  
Percentage Points ◽  
Anderson Darling ◽  
Von Mises

A class of goodness of fit tests for Marshal-Olkin Extended Rayleigh distribution with estimated parameters is proposed. The tests are based on the empirical distribution function. For determination of asymptotic percentage points, Kolomogorov-Sminrov, Cramer-von-Mises, Anderson-Darling,Watson, and Liao-Shimokawa test statistic are used. This article uses Monte Carlo simulations to obtain asymptotic percentage points for Marshal-Olkin extended Rayleigh distribution. Moreover, power of the goodness of fit test statistics is investigated for this lifetime model against several alternatives.

scholarly journals An Approach to the Quality of Drinking Water as a Matter of Multicriterial Decision

2021 ◽  
Vol 15 ◽  
pp. 17-24
Author(s):  
Amelia Bucur ◽  
Jose L. Lopez-Bonilla
Keyword(s):  
Mathematical Model ◽  
Water Quality ◽  
Drinking Water ◽  
Statistical Analysis ◽  
Quality Management ◽  
Mathematical Programming ◽  
Simulation Process ◽  
Percentage Points

The aim of the present paper is to approach the matter of water quality by resorting to the metod of multicriterial mathematical programming. MicrosoftExcel enables the simulation of a mathematical model. Furthermore, we have also created a file in the C++ software, in view of the simulation process, applicable to numberless properties of water quality. The case study presents the simulation of a multicriterial analysis of water quality in Sibiu county. This particular study shows the means of obtaining more information about water quality, subsequent to the analysis of its characteristics resorting to statistical analysis-specific software, e.g. SPSS 16 software. Given the increase of drinking water worldwide by tens of percentage points in cca two decades, the author(s) consider(s) that an approach to the quality management of drinking water should represent a key priority of society.

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