Автор: Davide Carpi (davide.carpi@gmail.com). Создано в рамках проекта SMath. Опубликовано пользователем smath.
Это проект с открытыми исходными кодами. Исходные коды опубликованы под лицензией MIT и доступны в публичном хранилище SVN.

Функциональность Statistical Tools

Версия 1.0.6824.32561

Функции

Дополнительные компоненты, добавляющие в программу SMath Studio новые математические функции, необходимые для решения задач из различных областей.

  1. Bessel("1:число", "2:число")
    Bessel function and derivatives of "1:number" order, evaluated in the "2:number" point; returns Jnu(x), J'nu(x), Ynu(x), and Y'nu(x).
  2. BesselJ("1:число", "2:число")
    Bessel function of the First Kind, of "1:number" order, evaluated in the "2:number" point.
  3. BesselY("1:число", "2:число")
    Bessel function of the Second Kind, of "1:number" order, evaluated in the "2:number" point.
  4. Beta("1:переменная", "2:переменная")
    Returns the Beta function of "1:variable" and "2:variable" positive parameters.
  5. BetaRegularized("1:переменная", "2:переменная", "3:переменная")
    Returns the Regularized Beta function evaluated in "1:variable" ∈[0;1], using "2:variable" and "3:variable" positive parameters.
  6. CDF.Binomial("1:число", "2:число")
    Returns the Binomial CDF of k successes with "1:number" trials and "2:number" success probability ∈[0;1] in each trial.
  7. CDF.Binomial("1:число", "2:число", "3:число")
    Returns the Binomial CDF value of "1:number" successes with "2:number" trials and "3:number" success probability ∈[0;1] in each trial.
  8. CDF.Cauchy("переменная")
    Returns the Standard Cauchy CDF (null location parameter and unitary scale parameter) evaluated in "1:variable" points.
  9. CDF.Cauchy("1:переменная", "2:число", "3:число")
    Returns the Cauchy CDF evaluated in "1:variable" points, using assigned "2:number" location parameter and the "3:number" scale parameter.
  10. CDF.ChiSquare("переменная")
    Returns the Χ² single degree of freedom CDF evaluated in "1:variable" points.
  11. CDF.ChiSquare("1:переменная", "2:число")
    Returns the Χ² CDF evaluated in "1:variable" points, using assigned "2:number" degrees of freedom.
  12. CDF.Exponential("переменная")
    Returns the Standard Exponential CDF (λ = 1) evaluated in "1:variable" points.
  13. CDF.Exponential("1:переменная", "2:число")
    Returns the Exponential CDF evaluated in "1:variable" points, using assigned "2:number" rate parameter.
  14. CDF.F("переменная")
    Returns the Fisher-Snedecor F single degree of freedom CDF evaluated in "1:variable".
  15. CDF.F("1:переменная", "2:число", "3:число")
    Returns the Fisher-Snedecor F CDF evaluated in "1:variable" points, using assigned "2:number" numerator and "3:number" denominator degrees of freedom.
  16. CDF.Geometric("1:переменная", "2:число")
    Returns the Geometric CDF of failures until the first success, for "1:variable" trials ∈[0;n] and single trial success probability "2:number" ∈(0;1].
  17. CDF.GeometricShifted("1:переменная", "2:число")
    Returns the Geometric Shifted CDF used for modeling the number of trials until the first success, for "1:variable" trials ∈[1;n] and single trial success probability "2:number" ∈(0;1].
  18. CDF.Normal("переменная")
    Returns the Standard Normal CDF (null mean and unitary standard deviation) evaluated in "1:variable" points.
  19. CDF.Normal("1:переменная", "2:число")
    Returns the Normal CDF evaluated in "1:variable" points, using assigned "2:number" mean and unitary standard deviation.
  20. CDF.Normal("1:переменная", "2:число", "3:число")
    Returns the Normal CDF evaluated in "1:variable" points, using assigned "2:number" mean and "3:number" as standard deviation.
  21. CDF.Poisson("переменная")
    Returns the Standard Poisson CDF (λ = 1) evaluated in "1:variable" points.
  22. CDF.Poisson("1:переменная", "2:число")
    Returns the Poisson CDF evaluated in "1:variable" points, using assigned "2:number" as expected value.
  23. CDF.Rayleigh("переменная")
    Returns the Standard Rayleigh CDF (σ = 1) evaluated in "1:variable" points.
  24. CDF.Rayleigh("1:переменная", "2:число")
    Returns the Rayleigh CDF evaluated in "1:variable" points, using assigned "2:number" as standard deviation.
  25. CDF.t("переменная")
    Returns the Student's t single degree of freedom CDF evaluated in "1:variable" points.
  26. CDF.t("1:переменная", "2:число")
    Returns the Student's t CDF evaluated in "1:variable" points, using assigned "2:number" degrees of freedom.
  27. CDF.Uniform("1:переменная", "2:число", "3:число")
    Returns the Uniform Continuous CDF evaluated in "1:variable" points, inside the ["2:number","3:number"] interval of values.
  28. CDF.UniformDiscrete("1:переменная", "2:число", "3:число")
    Returns the Uniform Discrete CDF evaluated in "1:variable" points, inside the ["2:number","3:number"] interval of values.
  29. CDF.Weibull("переменная")
    Returns the Standard Weibull CDF (λ = 1 and k = 1) evaluated in "1:variable" points.
  30. CDF.Weibull("1:переменная", "2:число", "3:число")
    Returns the Weibull CDF evaluated in "1:variable" points, using assigned "2:number" scale parameter and the "3:number" shape parameter.
  31. Dirac("переменная")
    Dirac delta function, evaluated in "1:variable" points.
  32. Dirac("1:переменная", "2:число")
    Dirac delta function, evaluated in "1:variable" points and shifted in the "2:number" point.
  33. erf("переменная")
    Error function, evaluated in "1:variable" points.
  34. erf("1:переменная", "2:число")
    Error function, evaluated in "1:variable" points and shifted in the "2:number" point.
  35. erfc("переменная")
    Complementary error function, evaluated in "1:variable" points.
  36. erfc("1:переменная", "2:число")
    Complementary error function, evaluated in "1:variable" points and shifted in the "2:number" point.
  37. erfinv("переменная")
    Inverse error function, evaluated in "1:variable" points.
  38. GammaRegularized.P("1:переменная", "2:переменная")
    Regularized Gamma function P(a,x):γ(a,x)/Γ(a).
  39. GammaRegularized.Q("1:переменная", "2:переменная")
    Regularized Gamma function Q(a,x):Γ(a,x)/Γ(a).
  40. GeometricMean("матрица")
    Returns the geometric mean from a sample.
  41. HarmonicMean("матрица")
    Returns the harmonic mean from a sample.
  42. Heaviside.D("переменная")
    Discrete Heaviside step function, evaluated in "1:variable" points.
  43. Heaviside.D("1:переменная", "2:число")
    Discrete Heaviside step function, evaluated in "1:variable" points and shifted in the "2:number" point.
  44. Heaviside("переменная")
    Heaviside step function, evaluated in "1:variable" points.
  45. Heaviside("1:переменная", "2:число")
    Heaviside step function, evaluated in "1:variable" points and shifted in the "2:number" point.
  46. ICDF.Binomial("1:число", "2:число", "3:число")
    Returns the Binomial quantile function for "1:number" probability values ∈[0;1] with "2:number" trials and "3:number" success probability ∈[0;1] in each trial.
  47. ICDF.Cauchy("переменная")
    Returns the Standard Cauchy quantile function (null location parameter and unitary scale parameter) evaluated for "1:variable" probability values ∈[0;1].
  48. ICDF.Cauchy("1:переменная", "2:число", "3:число")
    Returns the Cauchy quantile function evaluated for "1:variable" probability values ∈[0;1], using assigned "2:number" location parameter and the "3:number" scale parameter.
  49. ICDF.ChiSquare("переменная")
    Returns the single degree of freedom Χ² quantile function evaluated for "1:variable" probability values ∈[0;1].
  50. ICDF.ChiSquare("1:переменная", "2:число")
    Returns the single degree of freedom Χ² quantile function evaluated for "1:variable" probability values ∈[0;1], using assigned "2:number" degrees of freedom.
  51. ICDF.Exponential("переменная")
    Returns the Standard Exponential quantile function (λ = 1) evaluated for "1:variable" probability values ∈[0;1].
  52. ICDF.Exponential("1:переменная", "2:число")
    Returns the Exponential quantile function evaluated for "1:variable" probability values ∈[0;1], using assigned "2:number" rate parameter.
  53. ICDF.F("переменная")
    Returns the single degree of freedom Fisher-Snedecor F quantile function evaluated for "1:variable" probability values ∈[0;1].
  54. ICDF.F("1:переменная", "2:число", "3:число")
    Returns the single degree of freedom Fisher-Snedecor F quantile function evaluated for "1:variable" probability values ∈[0;1], "2:number" numerator and "3:number" denominator degrees of freedom.
  55. ICDF.Geometric("1:переменная", "2:число")
    Returns the Geometric quantile function, for "1:variable" probability values ∈(0;1] to observe n successes with single trial probability "2:number" ∈(0;1].
  56. ICDF.GeometricShifted("1:переменная", "2:число")
    Returns the Geometric Shifted quantile function used for modeling the number of trials until the first success, for "1:variable" probability values ∈(0;1] to observe n failures until the first success with single trial probability "2:number" ∈(0;1].
  57. ICDF.Normal("переменная")
    Returns the Standard Normal quantile function (null mean and unitary standard deviation) evaluated for "1:variable" probability values ∈[0;1].
  58. ICDF.Normal("1:переменная", "2:число")
    Returns the Normal quantile function evaluated for "1:variable" probability values ∈[0;1], using assigned "2:number" mean and unitary standard deviation.
  59. ICDF.Normal("1:переменная", "2:число", "3:число")
    Returns the Normal quantile function evaluated for "1:variable" probability values, using assigned "2:number" mean and "3:number" as standard deviation.
  60. ICDF.Poisson("переменная")
    Returns the Standard quantile function (λ = 1) evaluated for "1:variable" probability values.
  61. ICDF.Poisson("1:переменная", "2:число")
    Returns the Poisson quantile function evaluated for "1:variable" probability values ∈[0;1], using assigned "2:number" as expected value.
  62. ICDF.Rayleigh("переменная")
    Returns the Standard Rayleigh quantile function (σ = 1) evaluated for "1:variable" probability values ∈[0;1].
  63. ICDF.Rayleigh("1:переменная", "2:число")
    Returns the Rayleigh quantile function evaluated for "1:variable" probability values ∈[0;1], using assigned "2:number" as standard deviation.
  64. ICDF.t("переменная")
    Returns the Standard Student's t quantile function (ν = 1) evaluated for "1:variable" probability values ∈[0;1].
  65. ICDF.t("1:переменная", "2:число")
    Returns the Student's t quantile function evaluated for "1:variable" probability values ∈[0;1], using assigned "2:number" degrees of freedom (ν).
  66. ICDF.Uniform("1:переменная", "2:число", "3:число")
    Returns the Uniform Continuous quantile function evaluated for "1:variable" probability values ∈[0;1], inside the ["2:number","3:number"] interval of values.
  67. ICDF.UniformDiscrete("1:переменная", "2:число", "3:число")
    Returns the Uniform Discrete quantile function evaluated for "1:variable" probability values ∈[0;1], inside the ["2:number","3:number"] interval of values.
  68. ICDF.Weibull("переменная")
    Returns the Standard Weibull quantile function (λ = 1 and k = 1) evaluated for "1:variable" probability values ∈[0;1].
  69. ICDF.Weibull("1:переменная", "2:число", "3:число")
    Returns the Weibull quantile function evaluated for "1:variable" probability values ∈[0;1], using assigned "2:number" scale parameter and the "3:number" shape parameter.
  70. Intercept("1:матрица", "2:матрица")
    Returns the intercept of the straight line given by a simple linear regression from a data points "1:matrix","2:matrix".
  71. Kurtosis("матрица")
    Returns the β₂ kurtosis from a sample.
  72. KurtosisExcess("матрица")
    Returns the γ₂ kurtosis excess from a sample.
  73. Mean("матрица")
    Returns the arithmetic mean from a sample.
  74. Median("матрица")
    Returns the median value from a sample.
  75. Mode("матрица")
    Returns the mode value from a sample.
  76. Mode("1:матрица", "2:переменная")
    Returns the mode value from a sample and the number of occourrences.
  77. Moment("1:матрица", "2:число")
    Returns the "2:number"th central moment of a sample "1:matrix".
  78. pdf.Binomial("1:число", "2:число")
    Returns the Binomial pdf of k successes with "1:number" trials and "2:number" success probability ∈[0;1] in each trial.
  79. pdf.Binomial("1:число", "2:число", "3:число")
    Returns the Binomial pdf value of "1:number" successes with "2:number" trials and "3:number" success probability ∈[0;1] in each trial.
  80. pdf.Cauchy("переменная")
    Returns the Standard Cauchy pdf (null location parameter and unitary scale parameter) evaluated in "1:variable" points.
  81. pdf.Cauchy("1:переменная", "2:число", "3:число")
    Returns the Cauchy pdf evaluated in "1:variable" points, using assigned "2:number" location parameter and the "3:number" scale parameter.
  82. pdf.ChiSquare("переменная")
    Returns the Χ² single degree of freedom pdf evaluated in "1:variable" points.
  83. pdf.ChiSquare("1:переменная", "2:число")
    Returns the Χ² pdf evaluated in "1:variable" points, using assigned "2:number" degrees of freedom.
  84. pdf.Exponential("переменная")
    Returns the Standard Exponential pdf (λ = 1) evaluated in "1:variable" points.
  85. pdf.Exponential("1:переменная", "2:число")
    Returns the Exponential pdf in "1:variable" points, using assigned "2:number" rate parameter.
  86. pdf.F("переменная")
    Returns the Fisher-Snedecor F single degree of freedom pdf evaluated in "1:variable".
  87. pdf.F("1:переменная", "2:число", "3:число")
    Returns the Fisher-Snedecor F pdf evaluated in "1:variable" points, using assigned "2:number" numerator and "3:number" denominator degrees of freedom.
  88. pdf.Geometric("1:переменная", "2:число")
    Returns the Geometric pdf of failures until the first success, for "1:variable" trials ∈[0;n] and single trial success probability "2:number" ∈(0;1].
  89. pdf.GeometricShifted("1:переменная", "2:число")
    Returns the Geometric pdf used for modeling the number of trials until the first success, for "1:variable" trials ∈[1;n] and single trial success probability "2:number" ∈(0;1].
  90. pdf.Normal("переменная")
    Returns the Standard Normal pdf (null mean and unitary standard deviation) evaluated in "1:variable" points.
  91. pdf.Normal("1:переменная", "2:число")
    Returns the Normal pdf evaluated in "1:variable" points, using assigned "2:number" mean and unitary standard deviation.
  92. pdf.Normal("1:переменная", "2:число", "3:число")
    Returns the Normal pdf evaluated in "1:variable" points, using assigned "2:number" mean and "3:number" as standard deviation.
  93. pdf.Poisson("переменная")
    Returns the Standard Poisson pdf (λ = 1) evaluated in "1:variable" points.
  94. pdf.Poisson("1:переменная", "2:число")
    Returns the Poisson pdf evaluated in "1:variable" points, using assigned "2:number" as expected value.
  95. pdf.Rayleigh("переменная")
    Returns the Standard Rayleigh pdf (σ = 1) evaluated in "1:variable" points.
  96. pdf.Rayleigh("1:переменная", "2:число")
    Returns the Rayleigh pdf evaluated in "1:variable" points, using assigned "2:number" as standard deviation.
  97. pdf.t("переменная")
    Returns the Student's t single degree of freedom pdf evaluated in "1:variable" points.
  98. pdf.t("1:переменная", "2:число")
    Returns the Student's t pdf evaluated in "1:variable" points, using assigned "2:number" degrees of freedom.
  99. pdf.Uniform("1:переменная", "2:число", "3:число")
    Returns the Uniform Continuous pdf evaluated in "1:variable" points, inside the ["2:number","3:number"] interval of values.
  100. pdf.UniformDiscrete("1:переменная", "2:число", "3:число")
    Returns the Uniform Discrete pdf evaluated in "1:variable" points, inside the ["2:number","3:number"] interval of values.
  101. pdf.Weibull("переменная")
    Returns the Standard Weibull pdf (λ = 1 and k = 1) evaluated in "1:variable" points.
  102. pdf.Weibull("1:переменная", "2:число", "3:число")
    Returns the Weibull pdf evaluated in "1:variable" points, using assigned "2:number" scale parameter and the "3:number" shape parameter.
  103. Random.N("1:число", "2:число")
    Returns a random value between "1:number" and "2:number" with uniform distribution. "1:number" and "2:number" must be between -2147483648 and 2147483646.
  104. Random.N("1:число", "2:число", "3:число")
    Returns a vector containing "1:number" of random values between "2:number" and "3:number" with uniform distribution. "2:number" and "3:number" must be between -2147483648 and 2147483646.
  105. Random.N("1:число", "2:число", "3:число", "4:число")
    Returns a "1:number" x "2:number" rectangular matrix containing random values between "3:number" and "4:number" with uniform distribution. "3:number" and "4:number" must be between -2147483648 and 2147483646.
  106. Random("число")
    Returns a vector containing "1:number" of random values between 0 and 1 with uniform distribution.
  107. Random("1:число", "2:число")
    Returns a "1:number" x "2:number" rectangular matrix containing random values between 0 and 1 with uniform distribution.
  108. Skewness("матрица")
    Returns the g₁ skewness from a sample (biased).
  109. Slope("1:матрица", "2:матрица")
    Returns the slope of the straight line given by a simple linear regression from a data points "1:matrix","2:matrix".
  110. StdDev("матрица")
    Returns the unbiased standard deviation from a sample "1:matrix".
  111. Variance("матрица")
    Returns the unbiased variance from a sample "1:matrix".
  112. WeightedMean("1:матрица", "2:матрица")
    Returns the weighted arithmetic mean from a sample "1:matrix" and a corresponding weight "2:matrix".