﻿<?xml version="1.0" encoding="utf-8" standalone="yes"?>
<?application progid="SMath Studio Desktop" version="0.99.7251.32800"?>
<worksheet xmlns="http://smath.info/schemas/worksheet/1.0">
  <settings ppi="96">
    <identity>
      <id>4af6d330-66a2-4b46-ac51-064b578f95b7</id>
      <revision>53</revision>
    </identity>
    <calculation>
      <precision>2</precision>
      <exponentialThreshold>5</exponentialThreshold>
      <trailingZeros>false</trailingZeros>
      <significantDigitsMode>false</significantDigitsMode>
      <roundingMode>0</roundingMode>
      <fractions>decimal</fractions>
    </calculation>
    <pageModel active="true" viewMode="0" printGrid="false" printAreas="true" simpleEqualsOnly="false" printBackgroundImages="true">
      <paper id="1" orientation="Portrait" width="850" height="1100" />
      <margins left="39" right="39" top="49" bottom="49" />
      <header alignment="Center" color="#a9a9a9">&amp;[DATE] &amp;[TIME] - &amp;[FILENAME]</header>
      <footer alignment="Center" color="#a9a9a9">&amp;[PAGENUM] / &amp;[COUNT]</footer>
      <backgrounds />
    </pageModel>
    <dependencies>
      <assembly name="SMath Studio Desktop" version="0.99.7251.32800" guid="a37cba83-b69c-4c71-9992-55ff666763bd" />
      <assembly name="Math Region" version="0.99.7251.32800" guid="02f1ab51-215b-466e-a74d-5d8b1cf85e8d" />
      <assembly name="SpecialFunctions" version="1.12.7251.32800" guid="2814e667-4e12-48b1-8d51-194e480eabc5" />
      <assembly name="Writer Region" version="0.22.7200.15900" guid="5922d677-323f-4327-8c68-be902d8339ad" />
      <assembly name="Statistical Tools" version="1.0.6824.32561" guid="76f6e9f5-ac86-4ffb-9e4d-284c8daecaf9" />
    </dependencies>
  </settings>
  <regions type="content">
    <region left="783" top="9" width="411" height="32" color="#000000">
      <writer lang="eng"><![CDATA[<span style="font-family: 'Calibri'; font-size: 13pt; font-weight: normal; font-style: normal; color: Black; background-color: Transparent; vertical-align: baseline; text-align: left; margin-left: 0pt; text-indent: 0pt; line-height: 115%">
<div>If this is slightly increased to 13.25, we get α  &gt; 1, and no error </div></span>]]></writer>
    </region>
    <region left="9" top="45" width="93" height="190" color="#000000" fontSize="10">
      <math decimalPlaces="4">
        <input>
          <e type="operand">X</e>
          <e type="operand">30.4</e>
          <e type="operand">13.22</e>
          <e type="operand">63.9</e>
          <e type="operand">387.1</e>
          <e type="operand">330</e>
          <e type="operand">187.3</e>
          <e type="operand">495.9</e>
          <e type="operand">18</e>
          <e type="operand">163.3</e>
          <e type="operand">128.8</e>
          <e type="operand">10</e>
          <e type="operand">1</e>
          <e type="function" args="12">mat</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="198" top="45" width="237" height="27" color="#000000" fontSize="11">
      <math decimalPlaces="4">
        <input>
          <e type="operand">3</e>
          <e type="function" args="1">appVersion</e>
        </input>
        <result action="numeric">
          <e type="operand" style="string">0.99.7251</e>
        </result>
      </math>
    </region>
    <region left="126" top="63" width="50" height="24" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">278.7</e>
        </input>
      </math>
    </region>
    <region left="126" top="90" width="50" height="24" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">13.22</e>
        </input>
      </math>
    </region>
    <region left="198" top="90" width="210" height="33" color="#000000" bgColor="#cdff9b" fontSize="11">
      <math decimalPlaces="8">
        <input>
          <e type="operand">X.mean</e>
          <e type="operand">X</e>
          <e type="function" args="1">Mean</e>
          <e type="operator" args="2">:</e>
        </input>
        <result action="numeric">
          <e type="operand">181.792</e>
        </result>
      </math>
    </region>
    <region left="198" top="126" width="102" height="33" color="#000000" fontSize="11">
      <math optimize="2" decimalPlaces="4">
        <input>
          <e type="operand">LNX</e>
          <e type="operand">X</e>
          <e type="function" args="1">ln</e>
          <e type="function" args="1">vectorize</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="198" top="171" width="280" height="33" color="#000000" bgColor="#cdff9b" fontSize="11">
      <math decimalPlaces="9">
        <input>
          <e type="operand">LNX.mean</e>
          <e type="operand">LNX</e>
          <e type="function" args="1">Mean</e>
          <e type="operator" args="2">:</e>
        </input>
        <result action="numeric">
          <e type="operand">4.619457599</e>
        </result>
      </math>
    </region>
    <region left="198" top="216" width="300" height="34" color="#000000" bgColor="#cdff9b" fontSize="11">
      <math decimalPlaces="9">
        <input>
          <e type="operand">A</e>
          <e type="operand">X.mean</e>
          <e type="function" args="1">ln</e>
          <e type="operand">LNX.mean</e>
          <e type="operator" args="2">-</e>
          <e type="operator" args="2">:</e>
        </input>
        <result action="numeric">
          <e type="operand">0.583405577</e>
        </result>
      </math>
    </region>
    <region left="198" top="261" width="318" height="50" color="#000000" bgColor="#ffff80" fontSize="11">
      <math decimalPlaces="4">
        <input>
          <e type="operand">α</e>
          <e type="operand">1</e>
          <e type="operand">4</e>
          <e type="operand">A</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">/</e>
          <e type="operand">1</e>
          <e type="operand">1</e>
          <e type="operand">4</e>
          <e type="operand">A</e>
          <e type="operator" args="2">*</e>
          <e type="operand">3</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">+</e>
          <e type="function" args="1">sqrt</e>
          <e type="operator" args="2">+</e>
          <e type="bracket">(</e>
          <e type="operator" args="2">*</e>
          <e type="function" args="1">eval</e>
          <e type="operator" args="2">:</e>
        </input>
        <result action="numeric">
          <e type="operand">0.9999</e>
        </result>
      </math>
    </region>
    <region left="549" top="261" width="211" height="128" border="true" color="#000000">
      <writer lang="eng" wrap="Custom" width="197"><![CDATA[<span style="font-family: 'Arial'; font-size: 10pt; font-weight: normal; font-style: normal; color: Black; background-color: Transparent; vertical-align: baseline; text-align: left; margin-left: 0pt; text-indent: 0pt; line-height: 115%">
<div><span style="font-family: 'Bookman Old Style'"><span style="font-size: 11pt"><span style="background-color: #FFFFC6">Works correct only if <strong><span style="color: Red">numerically </span></strong>evaluated. </span></span></span></div>
<div><span style="font-family: 'Bookman Old Style'"><span style="font-size: 11pt"><span style="background-color: #FFFFC6">Otherwise gives different results in evaluating <strong>F &amp; G</strong> when using the <strong><span style="color: Red">vectorize </span></strong>operater ( <strong>only if α ≥ 1</strong> )</span></span></span></div></span>]]></writer>
    </region>
    <region left="198" top="324" width="223" height="52" color="#000000" bgColor="#ffff80" fontSize="11">
      <math decimalPlaces="4">
        <input>
          <e type="operand">β</e>
          <e type="operand">X.mean</e>
          <e type="operand">α</e>
          <e type="operator" args="2">/</e>
          <e type="function" args="1">eval</e>
          <e type="operator" args="2">:</e>
        </input>
        <result action="numeric">
          <e type="operand">181.8117</e>
        </result>
      </math>
    </region>
    <region left="54" top="360" width="91" height="25" color="#000000" fontSize="11">
      <math decimalPlaces="4">
        <input>
          <e type="operand">α</e>
        </input>
        <result action="numeric">
          <e type="operand">0.9999</e>
        </result>
      </math>
    </region>
    <region left="54" top="405" width="533" height="57" border="true" color="#000000">
      <writer lang="eng"><![CDATA[<span style="font-family: 'Calibri'; font-size: 13pt; font-weight: normal; font-style: normal; color: Black; background-color: Transparent; vertical-align: baseline; text-align: left; margin-left: 0pt; text-indent: 0pt; line-height: 115%">
<div style="text-align: justify">If  <strong>0 &lt; α &lt; 1</strong>  in <strong><span style="color: Red">Eqn 1</span></strong>  throwss an error . This behaviour seems to be a bug, either </div>
<div style="text-align: justify">in <strong>SS 7251</strong> OR evaluation of <strong>Eqn 1.  But it evaluates correctly in EXCEL</strong></div></span>]]></writer>
    </region>
    <region left="45" top="477" width="325" height="80" border="true" color="#000000" bgColor="#cbff97" fontSize="11">
      <math decimalPlaces="4">
        <input>
          <e type="operand">z</e>
          <e type="function" args="1">F</e>
          <e type="operand">1</e>
          <e type="operand">β</e>
          <e type="operand">α</e>
          <e type="operator" args="2">^</e>
          <e type="operand">α</e>
          <e type="function" args="1">Gamma</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">/</e>
          <e type="operand">x</e>
          <e type="operand">α</e>
          <e type="operand">1</e>
          <e type="operator" args="2">-</e>
          <e type="operator" args="2">^</e>
          <e type="operand">e</e>
          <e type="operand">x</e>
          <e type="operand">β</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="1">-</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">*</e>
          <e type="operand">x</e>
          <e type="operand">0</e>
          <e type="operand">z</e>
          <e type="function" args="4">int</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="396" top="504" width="51" height="32" color="#000000">
      <writer lang="eng"><![CDATA[<span style="font-family: 'Calibri'; font-size: 13pt; font-weight: normal; font-style: normal; color: Black; background-color: Transparent; vertical-align: baseline; text-align: left; margin-left: 0pt; text-indent: 0pt; line-height: 115%">
<div><strong><span style="color: Blue">Eqn 1</span></strong></div></span>]]></writer>
    </region>
    <region left="45" top="567" width="182" height="65" border="true" color="#000000" bgColor="#cbff97" fontSize="11">
      <math optimize="2" decimalPlaces="4">
        <description active="true" position="Top" lang="eng">
          <p fontName="Arial">Program 1</p>
        </description>
        <input>
          <e type="operand">j</e>
          <e type="operand">1</e>
          <e type="operand">X</e>
          <e type="function" args="1">rows</e>
          <e type="function" args="2">range</e>
          <e type="operand">G</e>
          <e type="operand">j</e>
          <e type="function" args="2">el</e>
          <e type="operand">X</e>
          <e type="operand">j</e>
          <e type="function" args="2">el</e>
          <e type="function" args="1">F</e>
          <e type="operator" args="2">:</e>
          <e type="function" args="1">eval</e>
          <e type="operand">1</e>
          <e type="operand">1</e>
          <e type="function" args="3">line</e>
          <e type="function" args="3">for</e>
        </input>
      </math>
    </region>
    <region left="315" top="576" width="86" height="38" color="#000000" fontSize="11">
      <math error="2" errorLocation="3" decimalPlaces="4">
        <input>
          <e type="operand">X</e>
          <e type="operand">3</e>
          <e type="function" args="2">el</e>
          <e type="function" args="1">F</e>
        </input>
        <result action="numeric">
          <e type="operand">#</e>
        </result>
      </math>
    </region>
    <region left="315" top="621" width="312" height="28" color="#000000" fontSize="13">
      <math>
        <input>
          <e type="operand">lastError</e>
        </input>
        <result action="numeric">
          <e type="operand" style="string">x - not defined.</e>
        </result>
      </math>
    </region>
    <region left="315" top="675" width="47" height="25" color="#000000" fontSize="11">
      <math error="2" errorLocation="0" decimalPlaces="4">
        <input>
          <e type="operand">G</e>
        </input>
        <result action="numeric">
          <e type="operand">#</e>
        </result>
      </math>
    </region>
    <region left="477" top="675" width="74" height="33" color="#000000" fontSize="11">
      <math error="2" decimalPlaces="4">
        <input>
          <e type="operand">X</e>
          <e type="function" args="1">F</e>
          <e type="function" args="1">vectorize</e>
        </input>
        <result action="numeric">
          <e type="operand">#</e>
        </result>
      </math>
    </region>
  </regions>
</worksheet>