{ "ns" : "http://zorba.io/modules/excel/statistical", "description" : " This is a library module offering a part of the set of statistical functions\n defined by Microsoft Excel 2003.\n", "sees" : [ "<xqdoc:see xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"><a href=\"http://office.microsoft.com/en-us/excel/CH062528311033.aspx\" target=\"_blank\">Excel 2003 Documentation: Statistical Functions</a></xqdoc:see>" ], "authors" : [ "<xqdoc:author xmlns:xqdoc=\"http://www.xqdoc.org/1.0\">Daniel Turcanu</xqdoc:author>" ], "version" : null, "encoding" : "utf-8", "namespaces" : [ { "uri" : "http://zorba.io/modules/excel/statistical", "prefix" : "excel" }, { "uri" : "http://zorba.io/modules/excel/errors", "prefix" : "excel-err" }, { "uri" : "http://zorba.io/modules/excel/math", "prefix" : "excel-math" }, { "uri" : "http://zorba.io/options/versioning", "prefix" : "ver" } ], "functions" : [ { "arity" : 1, "name" : "avedev", "qname" : "excel:avedev", "signature" : "($numbers as xs:anyAtomicType+) as xs:anyAtomicType", "description" : " Returns the average of the absolute deviations of data points from their mean.\n The formula is sum(abs(x - average_x))/n, where n is the count of x in the sequence.\n", "summary" : "<p> Returns the average of the absolute deviations of data points from their mean.</p>", "annotation_str" : "", "annotations" : [  ], "updating" : false, "parameters" : [ { "name" : "numbers", "type" : "xs:anyAtomicType", "occurence" : null, "description" : "<div xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"> the sequence of numbers or values castable to numeric. Sequence can be of any length from 1 up.</div>" } ], "returns" : { "type" : "xs:anyAtomicType", "description" : "The formula result" }, "errors" : [ "<xqdoc:error xmlns:xqdoc=\"http://www.xqdoc.org/1.0\">excel-err:Value if the parameters cannot be casted to numeric type</xqdoc:error>" ] }, { "arity" : 1, "name" : "average", "qname" : "excel:average", "signature" : "($numbers as xs:anyAtomicType*) as xs:anyAtomicType", "description" : " Returns the average (arithmetic mean) of the arguments.\n Arguments can be empty values, otherwise must be castable to numeric.\n If sequence is empty then zero is returned.\n The sequence can be of any length.\n", "summary" : "<p> Returns the average (arithmetic mean) of the arguments.</p>", "annotation_str" : "", "annotations" : [  ], "updating" : false, "parameters" : [ { "name" : "numbers", "type" : "xs:anyAtomicType", "occurence" : null, "description" : "<div xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"> The sequence of numbers or empty values.</div>" } ], "returns" : { "type" : "xs:anyAtomicType", "description" : "The sum of all numbers divided by the number of non-empty values." }, "errors" : [ "<xqdoc:error xmlns:xqdoc=\"http://www.xqdoc.org/1.0\">excel-err:Value if the parameters cannot be casted to numeric type.</xqdoc:error>" ] }, { "arity" : 1, "name" : "averagea", "qname" : "excel:averagea", "signature" : "($numbers as xs:anyAtomicType+) as xs:anyAtomicType", "description" : " Calculates the average (arithmetic mean) of the values in the sequence of arguments.\n Arguments can be of any type.\n The numbers are added, and the sum is divided by the size of entire sequence.\n", "summary" : "<p> Calculates the average (arithmetic mean) of the values in the sequence of arguments.</p>", "annotation_str" : "", "annotations" : [  ], "updating" : false, "parameters" : [ { "name" : "numbers", "type" : "xs:anyAtomicType", "occurence" : null, "description" : "<div xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"> the sequence of values of any type. The sequence can be of any length, from 1 up.</div>" } ], "returns" : { "type" : "xs:anyAtomicType", "description" : "The result" }, "errors" : [  ] }, { "arity" : 1, "name" : "count", "qname" : "excel:count", "signature" : "($numbers as xs:anyAtomicType*) as xs:integer", "description" : " Counts the number of cells that contain numbers or values castable to numeric.\n", "summary" : "<p> Counts the number of cells that contain numbers or values castable to numeric.</p>", "annotation_str" : "", "annotations" : [  ], "updating" : false, "parameters" : [ { "name" : "numbers", "type" : "xs:anyAtomicType", "occurence" : null, "description" : "<div xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"> The sequence of values, of any length.</div>" } ], "returns" : { "type" : "xs:integer", "description" : "The count of numbers." }, "errors" : [  ] }, { "arity" : 1, "name" : "counta", "qname" : "excel:counta", "signature" : "($numbers as xs:anyAtomicType*) as xs:integer", "description" : " Counts the number of values that are not empty.\n Empty values are the one with string value \"\".\n", "summary" : "<p> Counts the number of values that are not empty.</p>", "annotation_str" : "", "annotations" : [  ], "updating" : false, "parameters" : [ { "name" : "numbers", "type" : "xs:anyAtomicType", "occurence" : null, "description" : "<div xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"> the sequence of values of any type, any length</div>" } ], "returns" : { "type" : "xs:integer", "description" : "The count of non-empty values" }, "errors" : [  ] }, { "arity" : 1, "name" : "countblank", "qname" : "excel:countblank", "signature" : "($cells as xs:anyAtomicType*) as xs:integer", "description" : " Counts the empty values in a sequence.\n The empty values are the ones with string value \"\".\n The value 0 is not counted.\n", "summary" : "<p> Counts the empty values in a sequence.</p>", "annotation_str" : "", "annotations" : [  ], "updating" : false, "parameters" : [ { "name" : "cells", "type" : "xs:anyAtomicType", "occurence" : null, "description" : "<div xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"> the sequence of values, of any length</div>" } ], "returns" : { "type" : "xs:integer", "description" : "The count" }, "errors" : [  ] }, { "arity" : 2, "name" : "large", "qname" : "excel:large", "signature" : "($numbers as xs:anyAtomicType*, $k as xs:integer) as xs:anyAtomicType", "description" : " Returns the k-th largest value in a data set.\n If n is the number of data points in a range,\n   then LARGE(array,1) returns the largest value,\n   and LARGE(array,n) returns the smallest value.\n", "summary" : "<p> Returns the k-th largest value in a data set.</p>", "annotation_str" : "", "annotations" : [  ], "updating" : false, "parameters" : [ { "name" : "numbers", "type" : "xs:anyAtomicType", "occurence" : null, "description" : "<div xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"> the sequence of numbers or values castable to numeric. The sequence can be of any length, from 1 up.</div>" }, { "name" : "k", "type" : "xs:integer", "occurence" : null, "description" : "<div xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"> the position of largest value, with value from 1 to count of values</div>" } ], "returns" : { "type" : "xs:anyAtomicType", "description" : "The k-th largest value as numeric type" }, "errors" : [ "<xqdoc:error xmlns:xqdoc=\"http://www.xqdoc.org/1.0\">excel-err:Value if the parameters cannot be casted to numeric type</xqdoc:error>", "<xqdoc:error xmlns:xqdoc=\"http://www.xqdoc.org/1.0\">excel-err:Num if the sequence is empty</xqdoc:error>", "<xqdoc:error xmlns:xqdoc=\"http://www.xqdoc.org/1.0\">excel-err:Num if k is not a value between 1 and the sequence size</xqdoc:error>" ] }, { "arity" : 1, "name" : "max", "qname" : "excel:max", "signature" : "($numbers as xs:anyAtomicType*) as xs:anyAtomicType", "description" : " Returns the largest number in a sequence.\n", "summary" : "<p> Returns the largest number in a sequence.</p>", "annotation_str" : "", "annotations" : [  ], "updating" : false, "parameters" : [ { "name" : "numbers", "type" : "xs:anyAtomicType", "occurence" : null, "description" : "<div xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"> the sequence of numbers or values castable to numeric. The sequence can be of any length.</div>" } ], "returns" : { "type" : "xs:anyAtomicType", "description" : "The max" }, "errors" : [ "<xqdoc:error xmlns:xqdoc=\"http://www.xqdoc.org/1.0\">excel-err:Value if the parameters cannot be casted to numeric type</xqdoc:error>" ] }, { "arity" : 1, "name" : "maxa", "qname" : "excel:maxa", "signature" : "($numbers as xs:anyAtomicType*) as xs:anyAtomicType", "description" : " Returns the largest value in a list of arguments.\n In this implementation there is no difference between MAX and MAXA.\n", "summary" : "<p> Returns the largest value in a list of arguments.</p>", "annotation_str" : "", "annotations" : [  ], "updating" : false, "parameters" : [ { "name" : "numbers", "type" : "xs:anyAtomicType", "occurence" : null, "description" : "<div xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"> the sequence of numbers or values castable to numeric The sequence can be of any length.</div>" } ], "returns" : { "type" : "xs:anyAtomicType", "description" : "The max" }, "errors" : [ "<xqdoc:error xmlns:xqdoc=\"http://www.xqdoc.org/1.0\">excel-err:Value if the parameters cannot be casted to numeric type</xqdoc:error>" ] }, { "arity" : 1, "name" : "median", "qname" : "excel:median", "signature" : "($numbers as xs:anyAtomicType*) as xs:anyAtomicType", "description" : " Returns the median of the given numbers.\n The median is the number in the middle of a set of numbers.\n Half the numbers have values that are greater than the median,\n and half the numbers have values that are less than the median.\n", "summary" : "<p> Returns the median of the given numbers.</p>", "annotation_str" : "", "annotations" : [  ], "updating" : false, "parameters" : [ { "name" : "numbers", "type" : "xs:anyAtomicType", "occurence" : null, "description" : "<div xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"> the sequence of numbers, of any length</div>" } ], "returns" : { "type" : "xs:anyAtomicType", "description" : "for odd count of numbers return the number in the middle of the sorted sequence. For even count of numbers return the average of the two numbers in the middle." }, "errors" : [ "<xqdoc:error xmlns:xqdoc=\"http://www.xqdoc.org/1.0\">excel-err:Value if the parameters cannot be casted to numeric type</xqdoc:error>" ] }, { "arity" : 1, "name" : "min", "qname" : "excel:min", "signature" : "($numbers as xs:anyAtomicType*) as xs:anyAtomicType", "description" : " Returns the smallest number in a sequence.\n", "summary" : "<p> Returns the smallest number in a sequence.</p>", "annotation_str" : "", "annotations" : [  ], "updating" : false, "parameters" : [ { "name" : "numbers", "type" : "xs:anyAtomicType", "occurence" : null, "description" : "<div xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"> the sequence of numbers or values castable to numeric. The sequence can be of any length.</div>" } ], "returns" : { "type" : "xs:anyAtomicType", "description" : "The min" }, "errors" : [ "<xqdoc:error xmlns:xqdoc=\"http://www.xqdoc.org/1.0\">excel-err:Value if the parameters cannot be casted to numeric type</xqdoc:error>" ] }, { "arity" : 1, "name" : "mina", "qname" : "excel:mina", "signature" : "($numbers as xs:anyAtomicType*) as xs:anyAtomicType", "description" : " Returns the smallest value in a list of arguments.\n In this implementation there is no difference between MAX and MAXA.\n", "summary" : "<p> Returns the smallest value in a list of arguments.</p>", "annotation_str" : "", "annotations" : [  ], "updating" : false, "parameters" : [ { "name" : "numbers", "type" : "xs:anyAtomicType", "occurence" : null, "description" : "<div xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"> the sequence of numbers or values castable to numeric The sequence can be of any length.</div>" } ], "returns" : { "type" : "xs:anyAtomicType", "description" : "The min" }, "errors" : [ "<xqdoc:error xmlns:xqdoc=\"http://www.xqdoc.org/1.0\">excel-err:Value if the parameters cannot be casted to numeric type</xqdoc:error>" ] }, { "arity" : 1, "name" : "mode", "qname" : "excel:mode", "signature" : "($numbers as xs:anyAtomicType*) as xs:anyAtomicType", "description" : " Returns the most frequently occurring, or repetitive, value in a sequence.\n Arguments must be castable to numeric.\n", "summary" : "<p> Returns the most frequently occurring, or repetitive, value in a sequence.</p>", "annotation_str" : "", "annotations" : [  ], "updating" : false, "parameters" : [ { "name" : "numbers", "type" : "xs:anyAtomicType", "occurence" : null, "description" : "<div xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"> the sequence of numbers, of any length</div>" } ], "returns" : { "type" : "xs:anyAtomicType", "description" : "The most occuring number" }, "errors" : [ "<xqdoc:error xmlns:xqdoc=\"http://www.xqdoc.org/1.0\">excel-err:Value if the parameters cannot be casted to numeric type</xqdoc:error>", "<xqdoc:error xmlns:xqdoc=\"http://www.xqdoc.org/1.0\">fn:QName(\"http://zorba.io/modules/excel/errors\", \"excel-err:NA\") if there are no duplicate numbers</xqdoc:error>" ] }, { "arity" : 2, "name" : "percentile", "qname" : "excel:percentile", "signature" : "($numbers as xs:anyAtomicType*, $k_at as xs:anyAtomicType) as xs:anyAtomicType", "description" : " Returns the k-th percentile of values in a sequence.\n If k is not a multiple of 1/(n - 1),\n   PERCENTILE interpolates to determine the value at the k-th percentile.\n The function is computed by (max-min)*k + min\n", "summary" : "<p> Returns the k-th percentile of values in a sequence.</p>", "annotation_str" : "", "annotations" : [  ], "updating" : false, "parameters" : [ { "name" : "numbers", "type" : "xs:anyAtomicType", "occurence" : null, "description" : "<div xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"> the sequence of numbers, of any length</div>" }, { "name" : "k_at", "type" : "xs:anyAtomicType", "occurence" : null, "description" : "<div xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"> the percentile, with value between 0 .. 1 inclusive</div>" } ], "returns" : { "type" : "xs:anyAtomicType", "description" : "The computed percentile" }, "errors" : [ "<xqdoc:error xmlns:xqdoc=\"http://www.xqdoc.org/1.0\">excel-err:Value if the parameters cannot be casted to numeric type</xqdoc:error>", "<xqdoc:error xmlns:xqdoc=\"http://www.xqdoc.org/1.0\">excel-err:Num if percentile is not between 0 .. 1</xqdoc:error>" ] }, { "arity" : 2, "name" : "percentrank", "qname" : "excel:percentrank", "signature" : "($numbers as xs:anyAtomicType*, $x as xs:anyAtomicType) as xs:decimal", "description" : " Returns the rank of a value in a data set as a percentage of the data set.\n If x does not match one of the values in array,\n   PERCENTRANK interpolates to return the correct percentage rank. <p xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"/>\n The formula is uses: (RANK - 1) / (size - 1) .\n", "summary" : "<p> Returns the rank of a value in a data set as a percentage of the data set.</p>", "annotation_str" : "", "annotations" : [  ], "updating" : false, "parameters" : [ { "name" : "numbers", "type" : "xs:anyAtomicType", "occurence" : null, "description" : "<div xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"> the sequence of numbers or values castable to numbers. The sequence can be of any length, from 1 up.</div>" }, { "name" : "x", "type" : "xs:anyAtomicType", "occurence" : null, "description" : "<div xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"> is the value for which you want to know the rank</div>" } ], "returns" : { "type" : "xs:decimal", "description" : "The percentage of rank." }, "errors" : [ "<xqdoc:error xmlns:xqdoc=\"http://www.xqdoc.org/1.0\">excel-err:Value if the parameters cannot be casted to numeric type</xqdoc:error>", "<xqdoc:error xmlns:xqdoc=\"http://www.xqdoc.org/1.0\">excel-err:Num if the sequence is zero length</xqdoc:error>" ] }, { "arity" : 3, "name" : "prob", "qname" : "excel:prob", "signature" : "($x_range as xs:anyAtomicType+, $prob_range as xs:anyAtomicType+, $range_lower_limit as xs:anyAtomicType) as xs:anyAtomicType", "description" : " This is the same as above, only that upper_limit is not specified.\n The probability is computed only for range_lower_limit.\n", "summary" : "<p> This is the same as above, only that upper_limit is not specified.</p>", "annotation_str" : "", "annotations" : [  ], "updating" : false, "parameters" : [ { "name" : "x_range", "type" : "xs:anyAtomicType", "occurence" : null, "description" : "<div xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"> is the range of numeric values of x with which there are associated probabilities. This does not need to be ordered.</div>" }, { "name" : "prob_range", "type" : "xs:anyAtomicType", "occurence" : null, "description" : "<div xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"> is a set of probabilities associated with values in x_range.</div>" }, { "name" : "range_lower_limit", "type" : "xs:anyAtomicType", "occurence" : null, "description" : "<div xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"> is the value for which you want a probability.</div>" } ], "returns" : { "type" : "xs:anyAtomicType", "description" : "The probability of the range_lower_limit value" }, "errors" : [ "<xqdoc:error xmlns:xqdoc=\"http://www.xqdoc.org/1.0\">excel-err:Num if any probability is not between 0 and 1</xqdoc:error>", "<xqdoc:error xmlns:xqdoc=\"http://www.xqdoc.org/1.0\">excel-err:Num if the sum of probabilities is not equal to 1</xqdoc:error>", "<xqdoc:error xmlns:xqdoc=\"http://www.xqdoc.org/1.0\">excel-err:Value if any parameter is not castable to numeric</xqdoc:error>", "<xqdoc:error xmlns:xqdoc=\"http://www.xqdoc.org/1.0\">excel-err:Num if x_range and prob_range do not have the same number of values</xqdoc:error>" ] }, { "arity" : 4, "name" : "prob", "qname" : "excel:prob", "signature" : "($x_range as xs:anyAtomicType+, $prob_range as xs:anyAtomicType+, $range_lower_limit as xs:anyAtomicType, $upper_limit as xs:anyAtomicType) as xs:anyAtomicType", "description" : " Returns the probability that values in a range are between two limits.\n", "summary" : "<p> Returns the probability that values in a range are between two limits.</p>", "annotation_str" : "", "annotations" : [  ], "updating" : false, "parameters" : [ { "name" : "x_range", "type" : "xs:anyAtomicType", "occurence" : null, "description" : "<div xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"> is the range of numeric values of x with which there are associated probabilities. This does not need to be ordered.</div>" }, { "name" : "prob_range", "type" : "xs:anyAtomicType", "occurence" : null, "description" : "<div xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"> is a set of probabilities associated with values in x_range.</div>" }, { "name" : "range_lower_limit", "type" : "xs:anyAtomicType", "occurence" : null, "description" : "<div xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"> is the lower bound on the value for which you want a probability.</div>" }, { "name" : "upper_limit", "type" : "xs:anyAtomicType", "occurence" : null, "description" : "<div xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"> is the upper bound on the value for which you want a probability.</div>" } ], "returns" : { "type" : "xs:anyAtomicType", "description" : "The probability of the entire range" }, "errors" : [ "<xqdoc:error xmlns:xqdoc=\"http://www.xqdoc.org/1.0\">excel-err:Num if any probability is not between 0 and 1</xqdoc:error>", "<xqdoc:error xmlns:xqdoc=\"http://www.xqdoc.org/1.0\">excel-err:Num if the sum of probabilities is not equal to 1</xqdoc:error>", "<xqdoc:error xmlns:xqdoc=\"http://www.xqdoc.org/1.0\">excel-err:Value if any parameter is not castable to numeric</xqdoc:error>", "<xqdoc:error xmlns:xqdoc=\"http://www.xqdoc.org/1.0\">excel-err:Num if x_range and prob_range do not have the same number of values</xqdoc:error>" ] }, { "arity" : 2, "name" : "quartile", "qname" : "excel:quartile", "signature" : "($numbers as xs:anyAtomicType*, $quart as xs:integer) as xs:anyAtomicType", "description" : " Returns the quartile of a data set.\n", "summary" : "<p> Returns the quartile of a data set.</p>", "annotation_str" : "", "annotations" : [  ], "updating" : false, "parameters" : [ { "name" : "numbers", "type" : "xs:anyAtomicType", "occurence" : null, "description" : "<div xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"> sequence of numbers or values castable to numbers. The sequence can be of any length, from 1 up.</div>" }, { "name" : "quart", "type" : "xs:integer", "occurence" : null, "description" : "<div xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"> <dl>one of the values 0, 1, 2, 3, 4 with meaning: <dt>0</dt> <dd> compute minimum value</dd> <dt>1</dt> <dd> compute first quartile (25th percentile)</dd> <dt>2</dt> <dd> compute median value (50th percentile)</dd> <dt>3</dt> <dd> compute third quartile (75th percentile)</dd> <dt>4</dt> <dd> compute maximum value</dd></dl></div>" } ], "returns" : { "type" : "xs:anyAtomicType", "description" : "the computed quartile, as numeric type" }, "errors" : [ "<xqdoc:error xmlns:xqdoc=\"http://www.xqdoc.org/1.0\">excel-err:Value if the parameters cannot be casted to numeric type</xqdoc:error>", "<xqdoc:error xmlns:xqdoc=\"http://www.xqdoc.org/1.0\">excel-err:Num if the sequence is zero length</xqdoc:error>", "<xqdoc:error xmlns:xqdoc=\"http://www.xqdoc.org/1.0\">excel-err:Num if $quart is not one of the values 0, 1, 2, 3, 4</xqdoc:error>" ] }, { "arity" : 2, "name" : "rank", "qname" : "excel:rank", "signature" : "($x as xs:anyAtomicType, $numbers as xs:anyAtomicType*) as xs:decimal", "description" : " This RANK function is same as the above, only that $order_ascending is set by default to false.\n", "summary" : "<p> This RANK function is same as the above, only that $order_ascending is set by default to false.</p>", "annotation_str" : "", "annotations" : [  ], "updating" : false, "parameters" : [ { "name" : "x", "type" : "xs:anyAtomicType", "occurence" : null, "description" : "<div xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"> The number whose rank you want to find.</div>" }, { "name" : "numbers", "type" : "xs:anyAtomicType", "occurence" : null, "description" : "<div xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"> the sequence of numbers or values castable to numbers. The sequence can be of any length.</div>" } ], "returns" : { "type" : "xs:decimal", "description" : "The rank of $x." }, "errors" : [ "<xqdoc:error xmlns:xqdoc=\"http://www.xqdoc.org/1.0\">excel-err:Value if the parameters cannot be casted to numeric type.</xqdoc:error>" ] }, { "arity" : 3, "name" : "rank", "qname" : "excel:rank", "signature" : "($x as xs:anyAtomicType, $numbers as xs:anyAtomicType*, $order_ascending as xs:boolean) as xs:decimal", "description" : " Returns the rank of a number in a list of numbers.\n The rank of a number is its size relative to other values in a list.\n (If you were to sort the list, the rank of the number would be its position.)\n RANK gives duplicate numbers the same rank.\n", "summary" : "<p> Returns the rank of a number in a list of numbers.</p>", "annotation_str" : "", "annotations" : [  ], "updating" : false, "parameters" : [ { "name" : "x", "type" : "xs:anyAtomicType", "occurence" : null, "description" : "<div xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"> The number whose rank you want to find.</div>" }, { "name" : "numbers", "type" : "xs:anyAtomicType", "occurence" : null, "description" : "<div xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"> The sequence of numbers or values castable to numbers. The sequence can be of any length.</div>" }, { "name" : "order_ascending", "type" : "xs:boolean", "occurence" : null, "description" : "<div xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"> <dl>A boolean having the meaning: <dt>false</dt><dd>then rank the number as if the sequence was sorted in descending order.</dd> <dt>true</dt> <dd>then rank the number as if the sequence was sorted in ascending order.</dd></dl></div>" } ], "returns" : { "type" : "xs:decimal", "description" : "The rank of $x." }, "errors" : [ "<xqdoc:error xmlns:xqdoc=\"http://www.xqdoc.org/1.0\">excel-err:Value if the parameters cannot be casted to numeric type.</xqdoc:error>" ] }, { "arity" : 2, "name" : "slope", "qname" : "excel:slope", "signature" : "($known_y as xs:anyAtomicType+, $known_x as xs:anyAtomicType+) as xs:anyAtomicType", "description" : " Returns the slope of the linear regression line through data points in known_y's and known_x's.\n The slope is the vertical distance divided by the horizontal distance between\n   any two points on the line, which is the rate of change along the regression line.\n It computes the formula:<p xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"/>\n sum((x - average_x)(y - average_y)) / sum((x - average_x)^2)  <p xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"/>\n where average_x and average_y are computed with AVERAGE function.\n", "summary" : "<p> Returns the slope of the linear regression line through data points in known_y's and known_x's.</p>", "annotation_str" : "", "annotations" : [  ], "updating" : false, "parameters" : [ { "name" : "known_y", "type" : "xs:anyAtomicType", "occurence" : null, "description" : "<div xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"> the sequence of y numbers. The sequence can be of any length, from 1 up.</div>" }, { "name" : "known_x", "type" : "xs:anyAtomicType", "occurence" : null, "description" : "<div xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"> the sequence of x numbers. The sequence can be of any length, from 1 up.</div>" } ], "returns" : { "type" : "xs:anyAtomicType", "description" : "The slope value, as numeric type" }, "errors" : [ "<xqdoc:error xmlns:xqdoc=\"http://www.xqdoc.org/1.0\">excel-err:Value if any parameter cannot be casted to numeric</xqdoc:error>", "<xqdoc:error xmlns:xqdoc=\"http://www.xqdoc.org/1.0\">fn:QName(\"http://zorba.io/modules/excel/errors\", \"excel-err:NA\") if there are different numbers of x's and y's</xqdoc:error>", "<xqdoc:error xmlns:xqdoc=\"http://www.xqdoc.org/1.0\">fn:QName(\"http://zorba.io/modules/excel/errors\", \"excel-err:NA\") if any sequence is empty</xqdoc:error>", "<xqdoc:error xmlns:xqdoc=\"http://www.xqdoc.org/1.0\">excel-err:Div0 if all x's are equal</xqdoc:error>" ] }, { "arity" : 2, "name" : "small", "qname" : "excel:small", "signature" : "($numbers as xs:anyAtomicType*, $k as xs:integer) as xs:anyAtomicType", "description" : " This function computes the k-th smallest value in a data set.\n Use this function to return values with a particular relative standing in a data set.\n If n is the number of data points in array, SMALL(array,1) equals the smallest value,\n   and SMALL(array,n) equals the largest value.\n", "summary" : "<p> This function computes the k-th smallest value in a data set.</p>", "annotation_str" : "", "annotations" : [  ], "updating" : false, "parameters" : [ { "name" : "numbers", "type" : "xs:anyAtomicType", "occurence" : null, "description" : "<div xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"> A sequence of numbers or values castable to numeric. The sequence can be of any length, from 1 up.</div>" }, { "name" : "k", "type" : "xs:integer", "occurence" : null, "description" : "<div xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"> The position (from the smallest) in the sequence of data to return. Must have value between 1 and size of sequence.</div>" } ], "returns" : { "type" : "xs:anyAtomicType", "description" : "The k-th smallest value of $numbers." }, "errors" : [ "<xqdoc:error xmlns:xqdoc=\"http://www.xqdoc.org/1.0\">excel-err:Value if the parameters cannot be casted to numeric type.</xqdoc:error>", "<xqdoc:error xmlns:xqdoc=\"http://www.xqdoc.org/1.0\">excel-err:Num if the sequence is zero length.</xqdoc:error>", "<xqdoc:error xmlns:xqdoc=\"http://www.xqdoc.org/1.0\">excel-err:Num if $k is not a value between 1 and the size of sequence.</xqdoc:error>" ] }, { "arity" : 3, "name" : "standardize", "qname" : "excel:standardize", "signature" : "($x as xs:anyAtomicType, $mean as xs:anyAtomicType, $standard_dev as xs:anyAtomicType) as xs:double", "description" : " Returns a normalized value from a distribution characterized by mean and standard_dev.<p xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"/>\n The formula is (x - mean) / standard_dev .\n", "summary" : "<p> Returns a normalized value from a distribution characterized by mean and standard_dev.</p>", "annotation_str" : "", "annotations" : [  ], "updating" : false, "parameters" : [ { "name" : "x", "type" : "xs:anyAtomicType", "occurence" : null, "description" : "<div xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"> is the value you want to normalize</div>" }, { "name" : "mean", "type" : "xs:anyAtomicType", "occurence" : null, "description" : "<div xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"> is the arithmetic mean of the distribution.</div>" }, { "name" : "standard_dev", "type" : "xs:anyAtomicType", "occurence" : null, "description" : "<div xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"> is the standard deviation of the distribution.</div>" } ], "returns" : { "type" : "xs:double", "description" : "The normalized x, as numeric type" }, "errors" : [ "<xqdoc:error xmlns:xqdoc=\"http://www.xqdoc.org/1.0\">excel-err:Value if any parameter cannot be casted to numeric</xqdoc:error>", "<xqdoc:error xmlns:xqdoc=\"http://www.xqdoc.org/1.0\">excel-err:Num if standard_dev is a value smaller than zero or equal</xqdoc:error>" ] }, { "arity" : 1, "name" : "var", "qname" : "excel:var", "signature" : "($numbers as xs:anyAtomicType+) as xs:anyAtomicType", "description" : " Estimates variance based on a sample.<p xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"/>\n The formula is sum(x - average_x)^2 / (n - 1).<p xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"/>\n average_x is computed with AVERAGE function.<p xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"/>\n n is the count of numbers from the sequence, excluding empty values.\n", "summary" : "<p> Estimates variance based on a sample.</p>", "annotation_str" : "", "annotations" : [  ], "updating" : false, "parameters" : [ { "name" : "numbers", "type" : "xs:anyAtomicType", "occurence" : null, "description" : "<div xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"> the sequence of numbers or values castable to numeric. The sequence can be of any length, from 1 up.</div>" } ], "returns" : { "type" : "xs:anyAtomicType", "description" : "The variance, as numeric type" }, "errors" : [ "<xqdoc:error xmlns:xqdoc=\"http://www.xqdoc.org/1.0\">excel-err:Value if the parameters cannot be casted to numeric type</xqdoc:error>" ] }, { "arity" : 1, "name" : "vara", "qname" : "excel:vara", "signature" : "($numbers as xs:anyAtomicType+) as xs:anyAtomicType", "description" : " Estimates variance based on a sample.<p xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"/>\n The formula is sum(x - average_x)^2 / (n - 1).<p xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"/>\n average_x is computed with AVERAGE function.<p xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"/>\n n is the size of sequence, including empty values.<p xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"/>\n", "summary" : "<p> Estimates variance based on a sample.</p>", "annotation_str" : "", "annotations" : [  ], "updating" : false, "parameters" : [ { "name" : "numbers", "type" : "xs:anyAtomicType", "occurence" : null, "description" : "<div xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"> the sequence of numbers or values castable to numeric. The sequence can be of any length, from 1 up.</div>" } ], "returns" : { "type" : "xs:anyAtomicType", "description" : "The variance, as numeric type" }, "errors" : [ "<xqdoc:error xmlns:xqdoc=\"http://www.xqdoc.org/1.0\">excel-err:Value if the parameters cannot be casted to numeric type</xqdoc:error>" ] }, { "arity" : 1, "name" : "varp", "qname" : "excel:varp", "signature" : "($numbers as xs:anyAtomicType+) as xs:anyAtomicType", "description" : " Calculates variance based on the entire population.<p xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"/>\n The formula is sum(x - average_x)^2 / n.<p xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"/>\n average_x is computed with AVERAGE function.<p xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"/>\n n is the count of numbers from the sequence, excluding empty values.<p xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"/>\n", "summary" : "<p> Calculates variance based on the entire population.</p>", "annotation_str" : "", "annotations" : [  ], "updating" : false, "parameters" : [ { "name" : "numbers", "type" : "xs:anyAtomicType", "occurence" : null, "description" : "<div xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"> the sequence of numbers or values castable to numeric. The sequence can be of any length, from 1 up.</div>" } ], "returns" : { "type" : "xs:anyAtomicType", "description" : "The variance, as numeric type" }, "errors" : [ "<xqdoc:error xmlns:xqdoc=\"http://www.xqdoc.org/1.0\">excel-err:Value if the parameters cannot be casted to numeric type</xqdoc:error>" ] }, { "arity" : 1, "name" : "varpa", "qname" : "excel:varpa", "signature" : "($numbers as xs:anyAtomicType+) as xs:anyAtomicType", "description" : " Calculates variance based on the entire population.<p xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"/>\n The formula is sum(x - average_x)^2 / n.<p xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"/>\n average_x is computed with AVERAGE function.<p xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"/>\n n is the size of sequence, including empty values.<p xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"/>\n", "summary" : "<p> Calculates variance based on the entire population.</p>", "annotation_str" : "", "annotations" : [  ], "updating" : false, "parameters" : [ { "name" : "numbers", "type" : "xs:anyAtomicType", "occurence" : null, "description" : "<div xmlns:xqdoc=\"http://www.xqdoc.org/1.0\"> the sequence of numbers or values castable to numeric. The sequence can be of any length, from 1 up.</div>" } ], "returns" : { "type" : "xs:anyAtomicType", "description" : "The variance, as numeric type" }, "errors" : [ "<xqdoc:error xmlns:xqdoc=\"http://www.xqdoc.org/1.0\">excel-err:Value if the parameters cannot be casted to numeric type</xqdoc:error>" ] } ], "variables" : [  ] }