(************** Content-type: application/mathematica ************** Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 11614, 475]*) (*NotebookOutlinePosition[ 12616, 509]*) (* CellTagsIndexPosition[ 12486, 502]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["Bounded and unbounded Johnson distributions", "Title"], Cell[TextData[{ "This package demonstrates how to calculate statistical functionals of \ bounded (", Cell[BoxData[ \(TraditionalForm\`S\_B\)]], ") and unbounded (", Cell[BoxData[ \(TraditionalForm\`S\_U\)]], ") Johnson distributions." }], "Text"], Cell[TextData[{ "Author: Sergej V. Aksenov\n\nDepartment of Microbiology and Immunology\n\ University of Michigan\nAnn Arbor, MI 48109, USA\n", ButtonBox["aksenov@mac.com", ButtonData:>{ URL[ "mailto:aksenov@mac.com"], None}, ButtonStyle->"Hyperlink"] }], "Text"], Cell["Last updated 1 May 2002", "Text"], Cell[CellGroupData[{ Cell["Installation and initialization", "Section", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ "The package file ", StyleBox["JohnsonDistributions.m", "Input"], " should be located inside the ", StyleBox["JohnsonDistributions", "Input"], " directory. \nThe ", StyleBox["JohnsonDistributions", "Input"], " directory should be put in one of the canonical places for AddOns. \n\ Two recommended places are first inside the ", StyleBox["Mathematica", FontSlant->"Italic"], " distribution in:" }], "Text"], Cell[BoxData[ \(ToFileName[\ {$TopDirectory, \ "\", \ "\"}]\)], \ "Input"], Cell["a second in the preferences directory:", "Text"], Cell[BoxData[ \(ToFileName[\ {$PreferencesDirectory, \ "\", \ \ "\"}]\)], "Input"], Cell[TextData[{ "When one of these locations is used there is no need to set ", StyleBox["$Path", "Input"], " and the loading instructions are identical for all versions of ", StyleBox["Mathematica", FontSlant->"Italic"], "." }], "Text"], Cell[TextData[{ "The ", StyleBox["JohnsonDistributions` ", "Input"], "package can be loaded with" }], "Text"], Cell[TextData[{ "<<", StyleBox["JohnsonDistributions", "Input"], "`", StyleBox["JohnsonDistributions", "Input"], "`" }], "Input", AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell["Introduction", "Section"], Cell["Johnson distributions are defined by the following formulas:", "Text"], Cell["Assume that z is distributed as Normal(0,1) then", "Text"], Cell[BoxData[ \(x = sinh \((\(z - g\)\/d)\)\)], "DisplayFormula"], Cell[TextData[{ "is distributed as unbounded Johnson variate with shape parameters g and d \ (of Johnson system ", Cell[BoxData[ \(TraditionalForm\`S\_U\)]], ")," }], "Text"], Cell["and", "Text"], Cell[BoxData[ \(x = 1\/\(1 + \[ExponentialE]\^\(-\(\(z - g\)\/d\)\)\)\)], "DisplayFormula"], Cell[TextData[{ "is distributed as bounded Johnson variate with shape parameters g and d \ (of Johnson system ", Cell[BoxData[ \(TraditionalForm\`S\_B\)]], ")." }], "Text"], Cell["\<\ Reference: N. L. Johnson, Systems of frequency curves generated by methods of \ translation, Biometrika 36 (1-2): 149-176 1949\ \>", "Text"], Cell[TextData[{ "This package provides extension of standard ", StyleBox["Mathematica", FontSlant->"Italic"], " functions PDF, CDF, Quantile, ParameterQ, Domain, DomainQ, Random, \ RandomArray, Mean, Variance, StandardDeviation, Skewness, and Kurtosis to \ Unbounded and Bounded Johnson distributions." }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["Examples", "Section"], Cell[CellGroupData[{ Cell["Example 1", "Subsection"], Cell[TextData[StyleBox["In Example 1 we demonstrate calculations with \ Unbounded Johnson distribution.", FontWeight->"Bold"]], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(?UnboundedJohnsonDistribution\)\)], "Input"], Cell[BoxData[ \("UnboundedJohnsonDistribution[g,d] represents unbounded Johnson \ distribution with shape parameters g and d."\)], "Print", CellTags->"Info3229250472-1513849"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ 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