Difference between revisions of "User:Regina"

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;native language: German
 
;native language: German
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;active in project: de, qa. sc
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;active in project: de, qa, sc, graphics, LibreOffice, Apache OpenOffice
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;OOo user name: regina
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;user name: regina
 
;special interest: www.ooowiki.de
 
;special interest: www.ooowiki.de
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;email: rb.henschel@t-online.de
  
 
[[Anleitung]]
 
[[Anleitung]]
  
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==Sandbox==
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== ToDo ==
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=== Working on functions sides ===
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== CHISQDIST ==
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Calculates values for a &chi;<sup>2</sup>-distribution.
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=== Syntax ===
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<tt>'''CHISQDIST(x; k; Cumulative)'''</tt>
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: <tt>'''x'''</tt> is the number, at which you will evaluate the &chi;<sup>2</sup>-distribution.
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: <tt>'''k'''</tt> sets the degrees of freedom for the &chi;<sup>2</sup>-distribution
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::Constraint: k must be a positive integer
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: <tt>'''Cumulative'''</tt> is a logical value.
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: In the case <tt>Cumulative=TRUE()</tt> the cumulative distribution function is used, in the case <tt>Cumulative=FALSE()</tt> the probability density function. This parameter is optional. It is set to <tt>TRUE()</tt> if missing.
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=== Semantic ===
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<tt>'''CHISQDIST(x;k;FALSE())'''</tt> returns values of the probability density function for the &chi;<sup>2</sup>-distribution:
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:<math>=
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\begin{cases}
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0, & \textrm{if}\; x < 0 \\
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\displaystyle \frac {x^{\frac k 2 -1}\,\mathrm e^{- \frac x 2}} {2^{\frac k 2}\,\Gamma(\frac k 2) }, &  \textrm{if}\; x \ge 0
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\end{cases}
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</math>
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<tt>'''CHISQDIST(x;k;TRUE())'''</tt> returns the left tail probability for the &chi;<sup>2</sup>-distribution:
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:<math>=
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\begin{cases}
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0, & \textrm{if}\; x<0 \\
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\displaystyle \int_0^x \frac {t^{\frac k 2 -1}\,\mathrm e^{- \frac t 2}} {2^{\frac k 2}\,\Gamma(\frac k 2) }\,\mathrm d t, & \textrm{if}\; x \ge 0
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\end{cases}
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</math>
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=== Example ===
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<tt>'''CHSQDIST(2.7;3;FALSE())'''</tt>
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: returns approximately 0.1699395239
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<tt>'''CHSQDIST(2.7;3;TRUE())'''</tt>
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: returns approximately 0.5597727056
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=== Remarks ===
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If you need <tt>CHISQDIST(x;k;TRUE())</tt> with a non integer parameter k, then use <tt>GAMMADIST(x;k/2;2)</tt> instead.
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In the density case the internal calculation uses logarithmic- and exponential function, if x &gt;1425 or x &middot; k &gt; 1391000. Therefore it is less accurate then than in other cases.
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=== See also: ===
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[[Documentation/How_Tos/Calc: CHISQINV function|'''CHISQINV''']],
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[[Documentation/How_Tos/Calc: CHIDIST function|'''LEGACY.CHIDIST''']],
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[[Documentation/How_Tos/Calc: CHIINV function|'''LEGACY.CHIINV''']],
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[[Documentation/How_Tos/Calc: CHITEST function|'''CHITEST''']]
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[[Documentation/How_Tos/Calc: Statistical functions|'''Statistical functions''']]
 
[[Documentation/How_Tos/Calc: Statistical functions|'''Statistical functions''']]
  
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[[Documentation/How_Tos/Calc: Functions listed by category|'''Functions listed by category''']]
 
[[Documentation/How_Tos/Calc: Functions listed by category|'''Functions listed by category''']]
  
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=== Issues: ===
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[[Calc/ODFF_Implementation/Examine_functions|ODFF and accuracy problems in statitistic functions]]
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This function is expected for OOo3.1
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__NOTOC__
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[[Calc/Drafts/Treatment_of_new_Excel_2010_functions|Treatment of new Excel 2010 functions]]
  
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== CHISQINV ==
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=== Planning Wiki-Pages ===
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Calculates the inverse of the CHISQDIST function.
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[[/MyDrafts]] new document on ''Precision and Accuracy''
  
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=== Syntax ===
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[[/MYDrafts2]] new specification for print ranges
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<tt>'''CHISQINV(p; k)'''</tt>
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: <tt>'''k'''</tt> is the degrees of freedom for the &chi;<sup>2</sup>-distribution.
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:: Constraint: k must be a positive integer
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[[/MYDrafts3]] TTEST
  
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: <tt>'''p'''</tt> is the given probability
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[[/MYDrafts4]] Angle problems in ODF 1.2
  
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:: Constraint: 0 &le; p < 1
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[[/ComparisonWriterDrawPicture]] Comparison between Writer- and Draw-picture
  
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=== Semantic ===
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[[/MYDrafts5]] Custom Shapes
  
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: <tt>'''CHISQINV(p; k)'''</tt> returns the value <tt>'''x'''</tt>, such that <tt>'''CHISQDIST(x; k;TRUE())''' = '''p'''</tt>.
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=== Development ===
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Currently: Adding more font colors to Math [[/MYDrafts6]] Colors in Math
  
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=== Example ===
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== Sandbox ==
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<tt>'''CHISQINV(0.5; 9)'''</tt>
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=== math tests ===
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: returns approximately 8.342832692
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.
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=== Remarks ===
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[[http://meta.wikimedia.org/wiki/Help:Formula]]
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If you need <tt>CHISQINV(p;k)</tt> for a non interger parameter k, then use <tt>GAMMAINV(p;k/2;2)</tt> instead.
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=== See also: ===
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Test Wiki-markup here
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[[Documentation/How_Tos/Calc: CHISQDIST function|'''CHISQDIST''']]
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[[Documentation/How_Tos/Calc: CHIDIST function|'''CHIDIST''']]
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[[Documentation/How_Tos/Calc: CHIINV function|'''CHIINV''']]
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[[Documentation/How_Tos/Calc: Statistical functions|'''Statistical functions''']]
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<math>\sum_{k=1}^N k \pm i</math>
  
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[[Documentation/How_Tos/Calc: Functions listed alphabetically|'''Functions listed alphabetically''']],
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<math>a - b </math>
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[[Documentation/How_Tos/Calc: Functions listed by category|'''Functions listed by category''']]
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=== Issues: ===
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<math>a + b</math>
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* This function is expected for OOo3.1
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<math>{a \pm b}</math>
  
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== GAMMA ==
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<nowiki><math>\sum_{k=1}^N k^2</math></nowiki>
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Returns the values of the Gamma function.
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<math>\sum_{k=1}^N k^2</math>
  
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=== Syntax ===
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<math>\scriptstyle \sqrt {n-1}</math> <nowiki> <math>\scriptstyle \sqrt {n-1}</math> </nowiki>
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<tt>'''GAMMA(x)'''</tt>
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:<tt>'''x'''</tt> is a number.
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<math>\sqrt {n-1}</math> <nowiki><math>\sqrt {n-1}</math> </nowiki>  
  
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:: Constraint: If x is an integer, then x must be positive.
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<math> s_{X_1 - X_2}</math> <nowiki><math> s_{X_1 - X_2}</math> </nowiki>  
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=== Semantic ===
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<tt>'''GAMMA(x)'''</tt> calculates
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: <math>\Gamma(x) = \int_0^\infty t^{x-1} \mathrm e^{- t} \mathrm d t \,\!</math>.
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=== Example ===
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: <tt>'''GAMMA(4) = 6.0'''</tt> exact
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: <tt>'''GAMMA(34.56)''' &asymp; 6.2336323276E+037</tt>
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: <tt>'''GAMMA(&minus;4)'''</tt> not defined
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=== Remarks ===
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For x &lt; 0.5 Eulers reflection formula is used.
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The Gamma function has poles for negative integers and for zero. Near the poles the values are less accurate.
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If x is a positive integer, then
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: <math>\displaystyle \Gamma(x)=(x-1)\mathrm ! </math>
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But be aware, that OpenOffice.org has only a precision of 15 digits, therefore the results for x &gt; 21 are rounded.
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=== See also: ===
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[[Documentation/How_Tos/Calc: GAMMADIST function|'''GAMMALN''']],
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[[Documentation/How_Tos/Calc: GAMMAINV function|'''GAMMADIST''']],
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[[Documentation/How_Tos/Calc: GAMMAINV function|'''GAMMAINV''']],
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[[Documentation/How_Tos/Calc: GAMMAINV function|'''FACT''']]
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[[Documentation/How_Tos/Calc: Mathematical functions|'''Mathematical functions''']]
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[[Documentation/How_Tos/Calc: Statistical functions|'''Statistical functions''']]
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[[Documentation/How_Tos/Calc: Functions listed alphabetically|'''Functions listed alphabetically''']],
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[[Documentation/How_Tos/Calc: Functions listed by category|'''Functions listed by category''']]
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=== Issues: ===
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<math>1-P( -|z| \le Z \le |z|)</math> <nowiki> <math>1-P( -|z| \le Z \le |z|)</math> </nowiki>
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This function is expected for OOo3.1.
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== Accuracy ==
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<math>\textstyle \sum_{k=1}^N k^2</math> <nowiki> <math>\textstyle \sum_{k=1}^N k^2</math> </nowiki>
  
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=== Precision in Calc ===
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<math>\sum_{k=1}^N k^2</math> <nowiki> <math>\sum_{k=1}^N k^2</math> </nowiki>
  
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Calc uses for its calculation floating point numbers in double precision as defined in IEEE 754 standard. You get the best representation in a spreadsheet cell using the scientific format with format code <tt>0.00000000000000E+000</tt>. But because a binary format is used internally, the numbers in calculation might differ slightly from the shown decimal values. Only integers in the range <math>\scriptstyle -2^{53} \ldots 2^{53}</math> can be represented exactly in the internal format.
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<math>\int_{1}^{3}\frac{e^3/x}{x^2}\, dx</math> <nowiki> <math>\int_{1}^{3}\frac{e^3/x}{x^2}\, dx</math> </nowiki>
  
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Although you can force Calc to show 15 decimal digits, these might not be all accurate. This article lists some of the problems.
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<nowiki><math>\sum_{k=1}^N k^2</math></nowiki>
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<math>\sum_{k=1}^N k^2</math>
  
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=== Cancellation ===
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<math>\frac{1}{N} \sum_{k=2}^N k^2</math>
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<nowiki><math>\frac{1}{N} \sum_{k=2}^N k^2</math></nowiki>
  
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If you subtract two non integer numbers, which have nearly the same value, the result has less significant digits then the initial values.
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<math>\frac{1} {n} \sum_{i} {(x_i - \bar x)(y_i - \bar y)}</math>
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{| class="wikitable"
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<nowiki>\frac{1} {n} \sum_{i} {(x_i - \bar x)(y_i - \bar y)}</math></nowiki>
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|-
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! !! A !! B !! C
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|-
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! 1
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| 9.99411764795882E-001 || =0.999411764795882 ||
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|-
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! 2
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| 9.99411764705882E-001 || =1699/1700 || 
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|-
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! 3
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| 8.99997854020285E-011 || =A1-A2 ||
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|-
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! 4
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| 8.99996470588235E-011 ||  ||
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|}
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Cell A4 shows the correct result of <math>\scriptstyle 0.999411764795882-1699/1700</math>, calculated with a computer algebra system with 200 digits precision.
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=== dashboard ===

Latest revision as of 11:38, 23 October 2014

native language
German
active in project
de, qa, sc, graphics, LibreOffice, Apache OpenOffice
user name
regina
special interest
www.ooowiki.de
email
rb.henschel@t-online.de

Anleitung

ToDo

Working on functions sides

Statistical functions

Functions listed alphabetically, Functions listed by category

ODFF and accuracy problems in statitistic functions

Treatment of new Excel 2010 functions

Planning Wiki-Pages

/MyDrafts new document on Precision and Accuracy

/MYDrafts2 new specification for print ranges

/MYDrafts3 TTEST

/MYDrafts4 Angle problems in ODF 1.2

/ComparisonWriterDrawPicture Comparison between Writer- and Draw-picture

/MYDrafts5 Custom Shapes

Development

Currently: Adding more font colors to Math /MYDrafts6 Colors in Math

Sandbox

math tests

[[1]]

Test Wiki-markup here

<math>\sum_{k=1}^N k^2</math>

<math>\scriptstyle \sqrt {n-1}</math>

<math>\sqrt {n-1}</math>

<math> s_{X_1 - X_2}</math>

<math>1-P( -|z| \le Z \le |z|)</math>

<math>\textstyle \sum_{k=1}^N k^2</math>

<math>\sum_{k=1}^N k^2</math>

<math>\int_{1}^{3}\frac{e^3/x}{x^2}\, dx</math>

<math>\sum_{k=1}^N k^2</math>

<math>\frac{1}{N} \sum_{k=2}^N k^2</math>

\frac{1} {n} \sum_{i} {(x_i - \bar x)(y_i - \bar y)}</math>

dashboard

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