Packages

package stat

The stat package contains classes, traits and objects for basic statistical functions and analyses. The package object itself defines an implicit conversion from scalation.linalgebra.VectorD to StatVector.

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  1. class Anova extends AnyRef

    The Anova class provides the functions necessary for performing a one-way ANalysis Of VAriance (ANOVA) on the input data matrix x.

    The Anova class provides the functions necessary for performing a one-way ANalysis Of VAriance (ANOVA) on the input data matrix x. The data matrix: row i - i-th group/treatment column j - j-th replica

  2. class BatchVector extends AnyRef

    The BatchVector class contains a VectorD for maintaining experimental data in multiple batches and methods for computing statistics on these data.

    The BatchVector class contains a VectorD for maintaining experimental data in multiple batches and methods for computing statistics on these data. Ex: It can be used to support the Method of Batch Means (MBM).

  3. class Canvas extends Panel

    Create a canvas on which to draw the histogram.

  4. class FramelessHistogram extends AnyRef

    The FramelessHistogram class should be used in embedded applications.

  5. class GoodnessOfFit_CS extends Error

    The GoodnessOfFit_CS class is used to fit data to probability distributions.

    The GoodnessOfFit_CS class is used to fit data to probability distributions. Choosing the number of 'intervals' can be challenging and can affect the result: Suggestions: each interval should have 'E_i = n*p_i >= 5' and intervals >= sqrt (n). It uses the Chi-square goodness of fit test with equal width intervals.

    See also

    www.eg.bucknell.edu/~xmeng/Course/CS6337/Note/master/node66.html Compute the following for each interval and sum over all intervals. (O_i - E_i)^2 / E_i where O_i and E_i are the observed and expected counts for interval 'i', respectively.

  6. class GoodnessOfFit_CS2 extends Error

    The GoodnessOfFit_CS2 class is used to fit data to probability distributions.

    The GoodnessOfFit_CS2 class is used to fit data to probability distributions. Suggestions: each interval should have 'E_i = n*p_i >= 5' and intervals >= sqrt (n). It uses the Chi-square goodness of fit test with equal probability intervals.

    See also

    www.eg.bucknell.edu/~xmeng/Course/CS6337/Note/master/node66.html Compute the following for each interval and sum over all intervals. (O_i - E_i)^2 / E_i where O_i and E_i are the observed and expected counts for interval 'i', respectively.

  7. class GoodnessOfFit_KS extends Error

    The GoodnessOfFit_KS class is used to fit data to a probability distribution.

    The GoodnessOfFit_KS class is used to fit data to a probability distribution. It uses the Kolmogorov-Smirnov Goodness of Fit Test. Determine the maximum absolute difference 'd_max' between the data points 'd_i' and the theoretical value from a CDF F,

    d_max = max 1≤i≤n {|Fe(d_i) - F(d_i)|} (concept)

    d_max = max 1≤i≤n {F(d_i) − (i−1)/n, i/n − F(d_i)} (calculation)

    where 'Fe(.)' is the empirical distribution and 'F(.)' is the theoretical distribution. If 'd_max' is large, the fit should be rejected.

    See also

    www.eg.bucknell.edu/~xmeng/Course/CS6337/Note/master/node66.html

    www.itl.nist.gov/div898/handbook/eda/section3/eda35g.htm ---------------------------------------------------------------------------------

  8. class Histogram extends VizFrame

    The Histogram class takes a vector of values, counts the number of values in each of several intervals and displays the counts vertically in a histogram.

  9. final class MM_StatVector extends AnyVal

    The MM_StatVector value class provides methods for computing statistics on data vectors.

    The MM_StatVector value class provides methods for computing statistics on data vectors. Both maximum likelihood and unbiased estimators are supported. Unbiased should only be used on sample (not population) data. Ex: It can be used to support the Method of Independent Replications (MIR). For efficiency, MM_StatVector is a value class that enriches the VectorD. The corresponding implicit conversion in the stat package object.

    See also

    stackoverflow.com/questions/14861862/how-do-you-enrich-value-classes-without-overhead -----------------------------------------------------------------------------

  10. class StatTable extends Frame

    The StatTable class display statistical results in a frame's table.

  11. final class StatVector extends AnyVal

    The StatVector value class provides methods for computing statistics on data vectors.

    The StatVector value class provides methods for computing statistics on data vectors. Both maximum likelihood and unbiased estimators are supported. Unbiased should only be used on sample (not population) data. Ex: It can be used to support the Method of Independent Replications (MIR). For efficiency, StatVector is a value class that enriches the VectorD. The corresponding implicit conversion in the stat package object.

    See also

    stackoverflow.com/questions/14861862/how-do-you-enrich-value-classes-without-overhead -----------------------------------------------------------------------------

  12. final class StatVectorI extends AnyVal

    The StatVectorI value class provides methods for computing statistics on integer values data vectors.

    The StatVectorI value class provides methods for computing statistics on integer values data vectors. Both maximum likelihood and unbiased estimators are supported. Unbiased should only be used on sample (not population) data. For efficiency, StatVectorI is a value class that enriches the VectorI. The corresponding implicit conversion in the stat package object.

    See also

    stackoverflow.com/questions/14861862/how-do-you-enrich-value-classes-without-overhead -----------------------------------------------------------------------------

  13. class Statistic extends Error

    The Statistic class is used to collect values and compute sample statistics on them (e.g., waiting time).

    The Statistic class is used to collect values and compute sample statistics on them (e.g., waiting time). Contrast with TimeStatistic defined below.

  14. class T_Test extends AnyRef

    The T_Test class is used to test whether the means, 'μ1' and 'μ2', of two data samples, 'x' and 'y', are different, 'μ1 ≠ μ2', using a Two-Sample, Independent t-test.

    The T_Test class is used to test whether the means, 'μ1' and 'μ2', of two data samples, 'x' and 'y', are different, 'μ1 ≠ μ2', using a Two-Sample, Independent t-test. Assumes samples are drawn from Normal distributions. The error in the test is measured by the conditional probability 'p' that a "difference is detected" when there "actually is none".

    p = P(different | μ1 = μ2)

    The power of the test is the ability to detect actual differences. '1 - power' is measured by the conditional probability 'q' that a "difference is not detected" when there "actually is one".

    q = P(! different | μ1 ≠ μ2)

    These are called type I (measured by p) and type II (measured by q) errors.

    See also

    en.wikipedia.org/wiki/Type_I_and_type_II_errors -----------------------------------------------------------------------------

  15. class T_Test1 extends AnyRef

    The T_Test1 class is used to test whether a data sample 'x' comes from a population with "known" mean 'μ0', by comparing the sample mean 'μ' with 'μ0', using a (Two-Sided/Two-Tailed) One-Sample t-test.

    The T_Test1 class is used to test whether a data sample 'x' comes from a population with "known" mean 'μ0', by comparing the sample mean 'μ' with 'μ0', using a (Two-Sided/Two-Tailed) One-Sample t-test. Assumes the sample is drawn from a Normal distribution. The error in the test is measured by the conditional probability 'p' that a "difference is detected" when there "actually is none".

    p = P(different | μ = μ0)

    The power of the test is the ability to detect actual differences. '1 - power' is measured by the conditional probability 'p2' that a "difference is not detected" when there "actually is one".

    p2 = P(! different | μ ≠ μ0)

    These are called Type I (measured by p) and Type II (measured by p2) errors.

    See also

    en.wikipedia.org/wiki/Type_I_and_type_II_errors ----------------------------------------------------------------------------- H0: μ = μ0 Null Hypothesis H1: μ ≠ μ0 Alternative Hypothesis (Two-Sided) -----------------------------------------------------------------------------

  16. class TimeStatistic extends Statistic

    The TimeStatistic class is used to collect values and compute time-persistent statistics on them (e.g., Number in Queue).

    The TimeStatistic class is used to collect values and compute time-persistent statistics on them (e.g., Number in Queue).

    See also

    staff.unak.is/andy/Year%203%20Simulation/Laboratories/v4manual/internal.htm

Value Members

  1. implicit def vectorC2StatVector(x: VectorC): StatVector

    Implicit conversion from VectorD to StatVector, which supports more advanced statistical operations on vectors (e.g., covariance).

    Implicit conversion from VectorD to StatVector, which supports more advanced statistical operations on vectors (e.g., covariance). Other vector types require to conversion to VectorD via 'toDouble'. Caveat: won't work for vectors of string numbers (VectorS) since there not a meaningful conversion for general strings.

    x

    the vector to be enriched

  2. implicit def vectorD2StatVector(x: VectorD): StatVector
  3. implicit def vectorI2StatVector(x: VectorI): StatVectorI
  4. implicit def vectorL2StatVector(x: VectorL): StatVector
  5. implicit def vectorQ2StatVector(x: VectorQ): StatVector
  6. implicit def vectorR2StatVector(x: VectorR): StatVector
  7. implicit def vectorT2StatVector(x: VectorT): StatVector
  8. object AnovaTest extends App

    This object is used to test the Anova class.

    This object is used to test the Anova class.

    See also

    wiki.uiowa.edu/display/bstat/One-way+fixed+effects+ANOVA > runMain scalation.stat.AnovaTest

  9. object BatchVectorTest extends App

    The BatchVectorTest object provides an example of how to use the BatchVector class to implement the Method of Batch Means (MBM).

  10. object Conversions

    The Conversions object provide implicit conversion from memory mapped vectors to StatVectors.

  11. object GoodnessOfFit_CS

    The GoodnessOfFit_CS companion object provides two discrepancy metrics to capture the differences between observed 'o' and expected 'o' counts.

    The GoodnessOfFit_CS companion object provides two discrepancy metrics to capture the differences between observed 'o' and expected 'o' counts.

    See also

    en.wikipedia.org/wiki/G-test

  12. object GoodnessOfFit_CS2Test extends App

    The GoodnessOfFit_CS2Test object is used to test the GoodnessOfFit_CS class.

    The GoodnessOfFit_CS2Test object is used to test the GoodnessOfFit_CS class.

    See also

    www.seattlecentral.edu/qelp/sets/057/057.html > runMain scalation.stat.GoodnessOfFit_CS2Test

  13. object GoodnessOfFit_CSTest extends App

    The GoodnessOfFit_CSTest object is used to test the GoodnessOfFit_CS class.

    The GoodnessOfFit_CSTest object is used to test the GoodnessOfFit_CS class.

    See also

    www.seattlecentral.edu/qelp/sets/057/057.html > runMain scalation.stat.GoodnessOfFit_CSTest

  14. object GoodnessOfFit_KS

    The GoodnessOfFit_KS object provides methods to approximate the critical values/p-values for the KS Test.

    The GoodnessOfFit_KS object provides methods to approximate the critical values/p-values for the KS Test.

    P(D_n < d)

    See also

    www.jstatsoft.org/article/view/v008i18/kolmo.pdf

    sa-ijas.stat.unipd.it/sites/sa-ijas.stat.unipd.it/files/IJAS_3-4_2009_07_Facchinetti.pdf

  15. object GoodnessOfFit_KSTest extends App

    The GoodnessOfFit_KSTest object is used to test the GoodnessOfFit_KS class.

    The GoodnessOfFit_KSTest object is used to test the GoodnessOfFit_KS class.

    See also

    www.seattlecentral.edu/qelp/sets/057/057.html > runMain scalation.stat.GoodnessOfFit_KSTest

  16. object GoodnessOfFit_KSTest2 extends App

    The GoodnessOfFit_KSTest2 object is used to test the GoodnessOfFit_KS object.

    The GoodnessOfFit_KSTest2 object is used to test the GoodnessOfFit_KS object.

    See also

    www.utdallas.edu/~herve/Abdi-Lillie2007-pretty.pdf > runMain scalation.stat.GoodnessOfFit_KSTest2

  17. object GoodnessOfFit_KSTest3 extends App

    The GoodnessOfFit_KSTest3 object is used to test the GoodnessOfFit_KS object.

    The GoodnessOfFit_KSTest3 object is used to test the GoodnessOfFit_KS object.

    See also

    www.jstatsoft.org/article/view/v008i18/kolmo.pdf > runMain scalation.stat.GoodnessOfFit_KSTest3

  18. object GoodnessOfFit_KSTest4 extends App

    The GoodnessOfFit_KSTest4 object is used to test the GoodnessOfFit_KS object.

    The GoodnessOfFit_KSTest4 object is used to test the GoodnessOfFit_KS object. Fifty data points generated by a random variate generator for the Normal distribution are tested to see if they pass the Normality test. > runMain scalation.stat.GoodnessOfFit_KSTest4

  19. object HistogramTest extends App

    The HistogramTest object is used to test the Histogram class.

    The HistogramTest object is used to test the Histogram class. As 'k' increases, the sum of Uniform approaches Normal. > runMain scalation.stat.HistogramTest

  20. object MM_StatVectorTest extends App

    The MM_StatVectorTest object is used to test the MM_StatVector class.

    The MM_StatVectorTest object is used to test the MM_StatVector class. > runMain scalation.stat.MM_StatVectorTest

  21. object MM_StatVectorTest2 extends App

    The MM_StatVectorTest2 object provides an example of how to use the MM_StatVector class to implement the Method of Independent Replications (MIR) following a simple two-stage procedure.

  22. object MethodOfMoments

    The MethodOfMoments object provides methods for estimating parameters for popular probability distributions using the Method of Moments (MOM).

    The MethodOfMoments object provides methods for estimating parameters for popular probability distributions using the Method of Moments (MOM). The main alternative is to use Maximum Likelihood Estimators (MLE).

    See also

    www.math.uah.edu/stat/point/Moments.html

  23. object Normality

    The Normality object provides methods for testing Normality based on skewness and kurtosis.

    The Normality object provides methods for testing Normality based on skewness and kurtosis. Such test are more suitable for large sample sizes where more powerful goodness-of-fit tests tend to frequently reject Normality.

    See also

    stats.stackexchange.com/questions/29731/regression-when-the-ols-residuals-are-not-normally-distributed

    stats.stackexchange.com/questions/2492/is-normality-testing-essentially-useless

    en.wikipedia.org/wiki/D%27Agostino%27s_K-squared_test

  24. object NormalityTest extends App

    The NormalityTest object is used to test the Normality object.

    The NormalityTest object is used to test the Normality object.

    See also

    www.seattlecentral.edu/qelp/sets/057/057.html > runMain scalation.stat.NormalityTest

  25. object Probability extends Error

    The Probability object provides methods for operating on univariate and bivariate probability distributions of discrete random variables 'X' and 'Y'.

    The Probability object provides methods for operating on univariate and bivariate probability distributions of discrete random variables 'X' and 'Y'. A probability distribution is specified by its probability mass functions (pmf) stored either as a "probability vector" for a univariate distribution or a "probability matrix" for a bivariate distribution.

    joint probability matrix: pxy(i, j) = P(X = x_i, Y = y_j) marginal probability vector: px(i) = P(X = x_i) conditional probability matrix: px_y(i, j) = P(X = x_i|Y = y_j)

    In addition to computing joint, marginal and conditional probabilities, methods for computing entropy and mutual information are also provided. Entropy provides a measure of disorder or randomness. If there is little randomness, entropy will close to 0, while when randomness is high, entropy will be close to, e.g., 'log2 (px.dim)'. Mutual information provides a robust measure of dependency between random variables (contrast with correlation).

    See also

    scalation.stat.StatVector

  26. object ProbabilityTest extends App

    The ProbabilityTest object is used to test the Probability object.

    The ProbabilityTest object is used to test the Probability object. > runMain scalation.stat.ProbabilityTest

  27. object ProbabilityTest2 extends App

    The ProbabilityTest2 provides upper bound for 'entropy' and 'nentropy'.

    The ProbabilityTest2 provides upper bound for 'entropy' and 'nentropy'. > runMain scalation.stat.ProbabilityTest2

  28. object ProbabilityTest3 extends App

    The ProbabilityTest3 object is used to test the Probability class.

    The ProbabilityTest3 object is used to test the Probability class. Plot entropy. > runMain scalation.stat.ProbabilityTest3

  29. object ProbabilityTest4 extends App

    The ProbabilityTest4 object is used to test the Probability class.

    The ProbabilityTest4 object is used to test the Probability class. Plot probability and log-probability for binomial distributions. > runMain scalation.stat.ProbabilityTest4

  30. object ProbabilityTest5 extends App

    The ProbabilityTest5 object is used to test the Probability class.

    The ProbabilityTest5 object is used to test the Probability class. Plot entropy and normalize entropy for binomial distributions. > runMain scalation.stat.ProbabilityTest5

  31. object ProbabilityTest6 extends App

    The ProbabilityTest6 object is used to test the Probability class.

    The ProbabilityTest6 object is used to test the Probability class. It computes entropy, relative entropy and cross entropy and verifies thst cross entropy == entropy + relative entropy

    See also

    arxiv.org/pdf/0808.4111.pdf > runMain scalation.stat.ProbabilityTest6

  32. object ProbabilityTest7 extends App

    The ProbabilityTest7 object is used to test the Probability class.

    The ProbabilityTest7 object is used to test the Probability class. It computes joint, marginal and conditional probabilities as well as measures of independence.

    See also

    ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading7a.pdf > runMain scalation.stat.ProbabilityTest7

  33. object Q_Q_Plot extends Error

    The Q_Q_Plot object produces Quantile-Quantile plots that are used to compare probability distributions.

  34. object Q_Q_PlotTest extends App

    The Q_Q_PlotTest object is used to test the Q_Q_Plot object: distribution vs.

    The Q_Q_PlotTest object is used to test the Q_Q_Plot object: distribution vs. distribution. > runMain scalation.stat.Q_Q_PlotTest

  35. object Q_Q_PlotTest2 extends App

    The Q_Q_PlotTest2 object is used to test the Q_Q_Plot object: data vector vs.

    The Q_Q_PlotTest2 object is used to test the Q_Q_Plot object: data vector vs. distribution. > runMain scalation.stat.Q_Q_PlotTest2

  36. object StatTableTest extends App

    The StatTableTest is used to test the StatTable class.

  37. object StatVector

    The StatVector companion object extends statistics vector operations to matrices and convenience functions on vectors.

  38. object StatVectorITest extends App

    The StatVectorITest object is used to test the StatVectorI class.

    The StatVectorITest object is used to test the StatVectorI class.

    See also

    www.mathworks.com/help/stats/skewness.html > runMain scalation.stat.StatVectorITest

  39. object StatVectorTest extends App

    The StatVectorTest object is used to test the StatVector class.

    The StatVectorTest object is used to test the StatVector class.

    See also

    www.mathworks.com/help/stats/skewness.html > runMain scalation.stat.StatVectorTest

  40. object StatVectorTest2 extends App

    The StatVectorTest2 object provides an example of how to use the StatVector class to implement the Method of Independent Replications (MIR) following a simple two-stage procedure.

    The StatVectorTest2 object provides an example of how to use the StatVector class to implement the Method of Independent Replications (MIR) following a simple two-stage procedure. > runMain scalation.stat.StatVectorTest2

  41. object StatVectorTest3 extends App

    The StatVectorTest3 object is used to test the StatVector companion object by computing covariance, correlation and cosine matrices.

    The StatVectorTest3 object is used to test the StatVector companion object by computing covariance, correlation and cosine matrices.

    See also

    www.itl.nist.gov/div898/handbook/pmc/section5/pmc541.htm > runMain scalation.stat.StatVectorTest3

  42. object StatVectorTest4 extends App

    The StatVectorTest4 object is used to test the StatVector companion object by computing covariance, correlation and cosine matrices.

    The StatVectorTest4 object is used to test the StatVector companion object by computing covariance, correlation and cosine matrices.

    See also

    www.itl.nist.gov/div898/software/dataplot/refman2/auxillar/corrmatr.htm > runMain scalation.stat.StatVectorTest4

  43. object StatVectorTest5 extends App

    The StatVectorTest5 object is used to test the StatVector companion object by analyzing a time-series vector.

    The StatVectorTest5 object is used to test the StatVector companion object by analyzing a time-series vector. > runMain scalation.stat.StatVectorTest5

  44. object StatVectorTest6 extends App

    The StatVectorTest6 object is used to test the StatVector class by computing point and interval statistics on a data vector/sample.

    The StatVectorTest6 object is used to test the StatVector class by computing point and interval statistics on a data vector/sample.

    See also

    Data Science Using ScalaTion, Chapter 2, Example Problems > runMain scalation.stat.StatVectorTest6

  45. object StatVectorTest7 extends App

    The StatVectorTest7 object is used to test the StatVector class by computing point and interval statistics on a data vector/sample.

    The StatVectorTest7 object is used to test the StatVector class by computing point and interval statistics on a data vector/sample. It tests the success rates of confidence intervals based on the z- and t-distributions.

    See also

    Data Science Using ScalaTion, Chapter 2, Example Problems > runMain scalation.stat.StatVectorTest7

  46. object Statistic extends Error

    The Statistic companion object provides additional values and functions.

  47. object StatisticTest extends App

    The StatisticTest object is used to test the Statistic and TimeStatistic classes.

    The StatisticTest object is used to test the Statistic and TimeStatistic classes. > runMain scalation.stat.StatisticTest

  48. object T_Test

    The T_Test companion object provides a convenient method for performing t-test.

  49. object T_Test1

    The T_Test1 companion object provides a convenient method for performing t-test.

    The T_Test1 companion object provides a convenient method for performing t-test. If 'difference' is false (fail to reject), making a decision on this basis can be risky, so 'same' should be called. If neither 'different' or 'same' are true, need to collect more data.

  50. object T_Test1Test extends App

    The T_Test1Test object is used to test the T_Test1 class.

    The T_Test1Test object is used to test the T_Test1 class. > runMain scalation.stat.T_Test1Test

  51. object T_Test1Test2 extends App

    The T_Test1Test2 object is used to test the T_Test1 class.

    The T_Test1Test2 object is used to test the T_Test1 class.

    See also

    www.statsdirect.com/help/parametric_methods/single_sample_t.htm > runMain scalation.stat.T_Test1Test2

  52. object T_TestTest extends App

    The T_TestTest object is used to test the T_Test class.

    The T_TestTest object is used to test the T_Test class.

    See also

    www.isixsigma.com/tools-templates/hypothesis-testing/making-sense-two-sample-t-test/ > runMain scalation.stat.T_TestTest

  53. object TimeStatistic extends Error

    The TimeStatistic companion object provides additional functions.

Inherited from AnyRef

Inherited from Any

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