Sebaran Peluang Acak Kontinu, Distribusi Normal, Distribusi Normal Baku, Distribusi T, Distribusi Chi Square, dan Distribusi F

2020 ◽  
Author(s):  
Ahmad Sudi Pratikno
Keyword(s):  
Hypothesis Test ◽  
Standard Normal Distribution ◽  
Process Data ◽  
Nominal Data ◽  
Chi Square ◽  
Stable Curve ◽  
Standard Normal ◽  
Research Findings ◽  
F Distribution ◽  
T Distribution

In statistics, there are various terms that may feel unfamiliar to researcher who is not accustomed to discussing it. However, despite all of many functions and benefits that we can get as researchers to process data, it will later be interpreted into a conclusion. And then researcher can digest and understand the research findings. The distribution of continuous random opportunities illustrates obtaining opportunities with some detection of time, weather, and other data obtained from the field. The standard normal distribution represents a stable curve with zero mean and standard deviation 1, while the t distribution is used as a statistical test in the hypothesis test. Chi square deals with the comparative test on two variables with a nominal data scale, while the f distribution is often used in the ANOVA test and regression analysis.

scholarly journals A Simple Method for Generation of Statistical Tables by the Help of Excel Software

2011 ◽  
Vol 2 (1) ◽  
pp. 38-50
Author(s):  
Muhammad Irfan
Keyword(s):  
Normal Distribution ◽  
Poisson Distribution ◽  
Binomial Distribution ◽  
Standard Normal Distribution ◽  
Inverse Transformation ◽  
Chi Square ◽  
Easy Method ◽  
Simple Method ◽  
Standard Normal ◽  
F Distribution

A simple and easy method is employed to construct complete statistical tables like Student’s tdistribution, F distribution, Chi-square distribution and Cumulative standard normal distribution in Excel software which are used in all fields of research. Also, we generate other statistical tables like Cumulative binomial distribution, Cumulative Poisson distribution, Fisher transformation and Fisher inverse transformation. The proposed method depends only on the Excel software; it does not depend on the traditional statistical tables.

scholarly journals Chi-square, Student and Fisher-Snedecor Statistical Distributions and Their Application

2018 ◽  
Vol 80 (1) ◽  
pp. 16-23
Author(s):  
F. V. Motsnyi
Keyword(s):  
Probability Distributions ◽  
Point Of View ◽  
Experimental Results ◽  
Mathematical Statistics ◽  
Statistical Distributions ◽  
Chi Square ◽  
Chi Squared ◽  
Standard Normal ◽  
F Distribution ◽  
T Distribution

The Chi-square distribution is the distribution of the sum of squared standard normal deviates. The degree of freedom of the distribution is equal to the number of standard normal deviates being summed. For the first time this distribution was studied by astronomer F. Helmert in connection with Gaussian low of errors in 1876. Later K. Pearson named this function by Chi-square. Therefore Chi –square distribution bears a name of Pearson’s distribution. The Student's t-distribution is any member of a family of continuous probability distributions that arises when estimating the mean of a normally distributed population in situations where the sample size is small and population standard deviation is unknown. It was developed by W. Gosset in 1908. The Fisher–Snedecor distribution or F-distribution is the ratio of two-chi-squared variates. The F-distribution provides a basis for comparing the ratios of subsetsof these variances associated with different factors. The Fisher-distribution in the analysis of variance is connected with the name of R.Fisher (1924), although Fisher himself used quantity for the dispersion proportion. The Chi-square, Student and Fisher – Snedecor statistical distributions are connected enough tight with normal one. Therefore these distributions are used very extensively in mathematical statistics for interpretation of empirical data. The paper continues ideas of the author’s works [15, 16] devoted to advanced based tools of mathematical statistics. The aim of the work is to generalize the well known theoretical and experimental results of statistical distributions of random values. The Chi-square, Student and Fisher – Snedecor distributions are analyzed from the only point of view. The application peculiarities are determined at the examination of the agree criteria of the empirical sample one with theoretical predictions of general population. The numerical characteristics of these distributions are considered. The theoretical and experimental results are generalized. It is emphasized for the corrected amplification of the Chi-square, Student and Fisher – Snedecor distributions it is necessary to have the reliable empirical and testing data with the normal distribution.

scholarly journals AMSM- Sampling Distribution- Chapter Three

2018 ◽  
Author(s):  
Mohammed R. Dahman
Keyword(s):  
Limit Theorem ◽  
Comprehensive Analysis ◽  
Sampling Distribution ◽  
Sampling Strategies ◽  
Population Parameters ◽  
Chi Square ◽  
The Central Limit Theorem ◽  
F Distribution ◽  
The Common ◽  
T Distribution

Introduction of differences between population parameters and sample statistics are discussed. Followed with a comprehensive analysis of sampling distribution (i.e. definition, and properties). Then, we have discussed essential examiners (i.e. distribution): Z distribution, Chi square distribution, t distribution and F distribution. At the end, we have introduced the central limit theorem and the common sampling strategies.

scholarly journals MENENTUKAN PORTOFOLIO OPTIMAL MENGGUNAKAN MODEL CONDITIONAL MEAN VARIANCE

2016 ◽  
Vol 5 (3) ◽  
pp. 82
Author(s):  
I GEDE ERY NISCAHYANA ◽  
KOMANG DHARMAWAN ◽  
I NYOMAN WIDANA
Keyword(s):  
Standard Deviation ◽  
Stock Prices ◽  
Optimal Solution ◽  
Standard Normal Distribution ◽  
Variance Model ◽  
Conditional Mean ◽  
Standard Normal ◽  
The Mean ◽  
T Distribution ◽  
Mean Variance

When the returns of stock prices show the existence of autocorrelation and heteroscedasticity, then conditional mean variance models are suitable method to model the behavior of the stocks. In this thesis, the implementation of the conditional mean variance model to the autocorrelated and heteroscedastic return was discussed. The aim of this thesis was to assess the effect of the autocorrelated and heteroscedastic returns to the optimal solution of a portfolio. The margin of four stocks, Fortune Mate Indonesia Tbk (FMII.JK), Bank Permata Tbk (BNLI.JK), Suryamas Dutamakmur Tbk (SMDM.JK) dan Semen Gresik Indonesia Tbk (SMGR.JK) were estimated by GARCH(1,1) model with standard innovations following the standard normal distribution and the t-distribution.  The estimations were used to construct a portfolio. The portfolio optimal was found when the standard innovation used was t-distribution with the standard deviation of 1.4532 and the mean of 0.8023 consisting of 0.9429 (94%) of FMII stock, 0.0473 (5%) of  BNLI stock, 0% of SMDM stock, 1% of  SMGR stock.

scholarly journals Chebyshev–Edgeworth-Type Approximations for Statistics Based on Samples with Random Sizes

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 775
Author(s):  
Gerd Christoph ◽  
Vladimir V. Ulyanov
Keyword(s):  
Random Sample ◽  
Weighted Sums ◽  
Sample Sizes ◽  
Edgeworth Expansions ◽  
Chi Square ◽  
Limit Laws ◽  
Asymptotically Normal ◽  
Generalized Gamma ◽  
Standard Normal ◽  
T Distribution

Second-order Chebyshev–Edgeworth expansions are derived for various statistics from samples with random sample sizes, where the asymptotic laws are scale mixtures of the standard normal or chi-square distributions with scale mixing gamma or inverse exponential distributions. A formal construction of asymptotic expansions is developed. Therefore, the results can be applied to a whole family of asymptotically normal or chi-square statistics. The random mean, the normalized Student t-distribution and the Student t-statistic under non-normality with the normal limit law are considered. With the chi-square limit distribution, Hotelling’s generalized T02 statistics and scale mixture of chi-square distributions are used. We present the first Chebyshev–Edgeworth expansions for asymptotically chi-square statistics based on samples with random sample sizes. The statistics allow non-random, random, and mixed normalization factors. Depending on the type of normalization, we can find three different limit distributions for each of the statistics considered. Limit laws are Student t-, standard normal, inverse Pareto, generalized gamma, Laplace and generalized Laplace as well as weighted sums of generalized gamma distributions. The paper continues the authors’ studies on the approximation of statistics for randomly sized samples.

scholarly journals Alpha-Skew Generalized t Distribution

2015 ◽  
Vol 38 (2) ◽  
pp. 371-384 ◽  
Author(s):  
Sukru Acitas ◽  
Birdal Senoglu ◽  
Olcay Arslan
Keyword(s):  
Cumulative Distribution Function ◽  
Real Life ◽  
Likelihood Estimation ◽  
Point Of View ◽  
Cumulative Distribution ◽  
Standard Normal Distribution ◽  
Density Functions ◽  
Life Problems ◽  
Standard Normal ◽  
T Distribution

<p>The alpha-skew normal (ASN) distribution has been proposed recently in the literature by using standard normal distribution and a skewing approach. Although ASN distribution is able to model both skew and bimodal data, it is shortcoming when data has thinner or thicker tails than normal. Therefore, we propose an alpha-skew generalized t (ASGT) by using the generalized t (GT) distribution and a new skewing procedure. From this point of view, ASGT can be seen as an alternative skew version of GT distribution. However, ASGT differs from the previous skew versions of GT distribution since it is able to model bimodal data sest as well as it nests most commonly used density functions. In this paper, moments and maximum likelihood estimation of the parameters of ASGT distribution are given. Skewness and kurtosis measures are derived based on the first four noncentral moments. The cumulative distribution function (cdf) of ASGT distribution is also obtained. In the application part of the study, two real life problems taken from the literature are modeled by using ASGT distribution.</p>

INOVASI FONOLOGIS DENASALISASI DALAM ISOLEK BONAI ULAKPATIAN

2017 ◽  
Vol 6 (2) ◽  
pp. 235
Author(s):  
Yanti Riswara
Keyword(s):  
Historical Linguistic ◽  
Language Variation ◽  
Final Position ◽  
Process Data ◽  
Top Down ◽  
Linguistic Study ◽  
Oral Speech ◽  
Research Findings

The paper is aimed at describing a language variation, that is Ulakpatian Bonai isolect  in Riau Province. This is a kind of historical linguistic study which  is objected to describe a phonological inovation process of denasalisation among nasal phonemes at final positions or at close ultimate sillables in an isolect used by Bonai tribe in Ulakpatian, Rokan Hulu District,  Riau  Province.  Analysis  of  inavation is based on protomalayic (PM)  which  is reconstructed by Adelaar.The research applicates  top-down method of anaysis which are gaining  the  results by deductive process. Data of  this  research are oral  speech of Bonai people  based  on  200  Swadesh  words.  The  data  are  gathered  by  conversational  and listening  methods  which  applied  several  techniques.  The  results  of  the  analysis  are presented by formal and informal methods. The research findings reveal that the language of the tribe shows three kinds of denasalisation of phonological innovation at final position which  have  changed  the  nasal  phonemes  of  *PM  to  unnasal  ones  in  isolek  Bonai Ulakpatian: (*PM > BU) , i.e. 1) PM *n/-# > []/-#, 2) PM *m/-# > [p]/-#, dan 3) PM * /-# > [g]/-#.Abstrak  Makalah ini bertujuan untuk mendeskripsikan sebuah variasi bahasa, yaitu isolek Bonai Ulakpatian yang terdapat di Provinsi Riau. Kajian ini merupakan kajian linguistik historis yang memaparkan proses inovasi fonologis denasalisasi yang terjadi pada fonem-fonem nasal yang berada pada posisi akhir atau silabe ultima tertutup dalam sebuah isolek yang digunakan oleh suku Bonai di Desa Ulakpatian, Kabupaten Rokan Hulu. Analisis inovasi fonologis tersebut didasarkan pada protomalayik (PM) yang direkonstruksi oleh Adelaar. Kajian ini menerapkan mentode analisis top-down yang bersifat deduktif. Data penelitian merupakan data tuturan masyarakat suku Bonai yang mengacu pada 200 kosakata dasar yang dijadikan rujukan dalam penjaringan data kebahasaan. Data dikumpulkan dengan penerapan metode cakap dan metode simak dengan menggunakan teknik pancing dan teknik rekam. Data dideskripsikan secara fonetis dengan simbol IPA. Hasil penelitian disajikan dengan metode formal dan informal. Hasil penelitian menunjukkan bahwa isolek Bonai Ulakpatian memiliki tiga bentuk inovasi fonologis denasalisasi pada posisi akhir beberapa fonem nasal *PM menjadi taknasal pada isolek BU (*PM > BU) , yaitu 1) PM *n/-# > []/-#, 2) PM *m/-# > [p]/-#, dan 3) PM * /-# > [g]/-#.

scholarly journals Interpretable Variational Graph Autoencoder with Noninformative Prior

2021 ◽  
Vol 13 (2) ◽  
pp. 51
Author(s):  
Lili Sun ◽  
Xueyan Liu ◽  
Min Zhao ◽  
Bo Yang
Keyword(s):  
Latent Variables ◽  
Latent Variable ◽  
Expert Knowledge ◽  
Structural Information ◽  
Standard Normal Distribution ◽  
Noninformative Prior ◽  
Latent Space ◽  
Distribution Parameters ◽  
Standard Normal ◽  
Low Dimensional

Variational graph autoencoder, which can encode structural information and attribute information in the graph into low-dimensional representations, has become a powerful method for studying graph-structured data. However, most existing methods based on variational (graph) autoencoder assume that the prior of latent variables obeys the standard normal distribution which encourages all nodes to gather around 0. That leads to the inability to fully utilize the latent space. Therefore, it becomes a challenge on how to choose a suitable prior without incorporating additional expert knowledge. Given this, we propose a novel noninformative prior-based interpretable variational graph autoencoder (NPIVGAE). Specifically, we exploit the noninformative prior as the prior distribution of latent variables. This prior enables the posterior distribution parameters to be almost learned from the sample data. Furthermore, we regard each dimension of a latent variable as the probability that the node belongs to each block, thereby improving the interpretability of the model. The correlation within and between blocks is described by a block–block correlation matrix. We compare our model with state-of-the-art methods on three real datasets, verifying its effectiveness and superiority.

Sign in / Sign up

Export Citation Format

Share Document