Created by Davide Carpi (davide.carpi@gmail.com) in the scope of SMath project. Published by smath.
This is Open Source project. Sources shared under MIT Licence and available in public SVN repository.

Features of Statistical Tools

Version 1.0.6824.32561

Functions

Additional components that add new mathematical functions to the SMath Studio program, necessary for solving problems from various fields.

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