Parametric statistics - wikipedia Parametric statistics Parametric statistics is a branch of statistics which assumes that sample data comes from a population that follows a probability distribution based on a fixed set of parameters. Most well - known elementary statistical methods are parametric. Conversely a non-parametric model differs precisely in that the parameter set ( or feature set in machine learning ) is not fixed and can increase, or even decrease if new relevant information is collected. Since a parametric model relies on a fixed parameter set, it assumes more about a given population than non-parametric methods do. When the assumptions are correct, parametric methods will produce more accurate and precise estimates than non-parametric methods, i.e. have more statistical power. However, as more is assumed by parametric methods, when the assumptions are not correct they have a greater chance of failing, and for this reason are not robust statistical methods. On the other hand, parametric formulae are often simpler to write down and faster to compute. For this reason their simplicity can make up for their lack of robustness, especially if care is taken to examine diagnostic statistics. Contents 1 Example 2 History 3 See also 4 References Example The normal family of distributions all have the same general shape and are parameterized by mean and standard deviation. That means that if the mean and standard deviation are known and if the distribution is normal, the probability of any future observation lying in a given range is known. Suppose we have a sample of 99 test scores with a mean of 100 and a standard deviation of 1. If we assume all 99 test scores are random observations from a normal distribution, then we predict there is a 1 % chance that the 100th test score will be higher than 102.365 ( that is, the mean plus 2.365 standard deviations ) assuming that the 100th test score comes from the same distribution as the others. Parametric statistical methods are used to compute the 2.365 value above, given 99 independent observations from the same normal distribution. A non-parametric estimate of the same thing is the maximum of the first 99 scores. We do n't need to assume anything about the distribution of test scores to reason that before we gave the test it was equally likely that the highest score would be any of the first 100. Thus there is a 1 % chance that the 100th is higher than any of the 99 that preceded it. History Parametric functions were mentioned by R. Fisher in his work Statistical Methods for Research Workers in 1925 which created the foundation for modern statistics. See also Parametric equation Parametric model References Jump up ^ Geisser, S. ; Johnson, W.M. ( 2006 ) Modes of Parametric Statistical Inference, John Wiley & Sons, ISBN 978 - 0 - 471 - 66726 - 1 Jump up ^ Cox, D.R. ( 2006 ) Principles of Statistical Inference, Cambridge University Press, ISBN 978 - 0 - 521 - 68567 - 2 Jump up ^ Murphy, Kevin ( 2012 ). Machine Learning : A Probabilistic Perspective. MIT. p. 16. ISBN 978 - 0262018029. Jump up ^ Corder ; Foreman ( 2009 ) Nonparametric Statistics for Non-Statisticians : A Step - by - Step Approach, John Wiley & Sons, ISBN 978 - 0 - 470 - 45461 - 9 Jump up ^ Freedman, D. ( 2000 ) Statistical Models : Theory and Practice, Cambridge University Press, ISBN 978 - 0 - 521 - 67105 - 7 hide Statistics Outline Index Descriptive statistics Continuous data Center Mean arithmetic geometric harmonic Median Mode Dispersion Variance Standard deviation Coefficient of variation Percentile Range Interquartile range Shape Central limit theorem Moments Skewness Kurtosis L - moments Count data Index of dispersion Summary tables Grouped data Frequency distribution Contingency table Dependence Pearson product - moment correlation Rank correlation Spearman 's rho Kendall 's tau Partial correlation Scatter plot Graphics Bar chart Biplot Box plot Control chart Correlogram Fan chart Forest plot Histogram Pie chart Q -- Q plot Run chart Scatter plot Stem - and - leaf display Radar chart Data collection Study design Population Statistic Effect size Statistical power Sample size determination Missing data Survey methodology Sampling stratified cluster Standard error Opinion poll Questionnaire Controlled experiments Design control optimal Controlled trial Randomized Random assignment Replication Blocking Interaction Factorial experiment Uncontrolled studies Observational study Natural experiment Quasi-experiment hide Statistical inference Statistical theory Population Statistic Probability distribution Sampling distribution Order statistic Empirical distribution Density estimation Statistical model L space Parameter location scale shape Parametric family Likelihood ( monotone ) Location -- scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V Optimal decision loss function Efficiency Statistical distance divergence Asymptotics Robustness Frequentist inference Point estimation Estimating equations Maximum likelihood Method of moments M - estimator Minimum distance Unbiased estimators Mean - unbiased minimum - variance Rao -- Blackwellization Lehmann -- Scheffé theorem Median unbiased Plug - in Interval estimation Confidence interval Pivot Likelihood interval Prediction interval Tolerance interval Resampling Bootstrap Jackknife Testing hypotheses 1 - & 2 - tails Power Uniformly most powerful test Permutation test Randomization test Multiple comparisons Parametric tests Likelihood - ratio Wald Score Specific tests Z - test ( normal ) Student 's t - test F - test Goodness of fit Chi - squared G - test Kolmogorov -- Smirnov Anderson -- Darling Lilliefors Jarque -- Bera Normality ( Shapiro -- Wilk ) Likelihood - ratio test Model selection Cross validation AIC BIC Rank statistics Sign Sample median Signed rank ( Wilcoxon ) Hodges -- Lehmann estimator Rank sum ( Mann -- Whitney ) Nonparametric anova 1 - way ( Kruskal -- Wallis ) 2 - way ( Friedman ) Ordered alternative ( Jonckheere -- Terpstra ) Bayesian inference Bayesian probability prior posterior Credible interval Bayes factor Bayesian estimator Maximum posterior estimator Correlation Regression analysis Correlation Pearson product - moment Partial correlation Confounding variable Coefficient of determination Regression analysis Errors and residuals Regression model validation Mixed effects models Simultaneous equations models Multivariate adaptive regression splines ( MARS ) Linear regression Simple linear regression Ordinary least squares General linear model Bayesian regression Non-standard predictors Nonlinear regression Nonparametric Semiparametric Isotonic Robust Heteroscedasticity Homoscedasticity Generalized linear model Exponential families Logistic ( Bernoulli ) / Binomial / Poisson regressions Partition of variance Analysis of variance ( ANOVA, anova ) Analysis of covariance Multivariate ANOVA Degrees of freedom Categorical / Multivariate / Time - series / Survival analysis Categorical Cohen 's kappa Contingency table Graphical model Log - linear model McNemar 's test Multivariate Regression Manova Principal components Canonical correlation Discriminant analysis Cluster analysis Classification Structural equation model Factor analysis Multivariate distributions Elliptical distributions Normal Time - series General Decomposition Trend Stationarity Seasonal adjustment Exponential smoothing Cointegration Structural break Granger causality Specific tests Dickey -- Fuller Johansen Q - statistic ( Ljung -- Box ) Durbin -- Watson Breusch -- Godfrey Time domain Autocorrelation ( ACF ) partial ( PACF ) Cross-correlation ( XCF ) ARMA model ARIMA model ( Box -- Jenkins ) Autoregressive conditional heteroskedasticity ( ARCH ) Vector autoregression ( VAR ) Frequency domain Spectral density estimation Fourier analysis Wavelet Whittle likelihood Survival Survival function Kaplan -- Meier estimator ( product limit ) Proportional hazards models Accelerated failure time ( AFT ) model First hitting time Hazard function Nelson -- Aalen estimator Test Log - rank test Applications Biostatistics Bioinformatics Clinical trials / studies Epidemiology Medical statistics Engineering statistics Chemometrics Methods engineering Probabilistic design Process / quality control Reliability System identification Social statistics Actuarial science Census Crime statistics Demography Econometrics National accounts Official statistics Population statistics Psychometrics Spatial statistics Cartography Environmental statistics Geographic information system Geostatistics Kriging Portal Commons WikiProject Retrieved from `` https://en.wikipedia.org/w/index.php?title=Parametric_statistics&oldid=839226075 '' Categories : Parametric statistics Statistical inference Hidden categories : Use dmy dates from November 2015 Talk Contents Interaction About Wikipedia Català Deutsch Español فارسی Italiano Nederlands Português Simple English Basa Sunda Türkçe 4 more Edit links This page was last edited on 2 May 2018, at 02 : 51 ( UTC ). 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Question: the collection of statistical methods that require assumptions about the population is known as
Answer: Parametric statistics