ceph/src/boost/libs/math/doc/equations/hypergeometric6.mml

   1 <?xml version="1.0" encoding="UTF-8"?>
   2 <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1 plus MathML 2.0//EN" "http://www.w3.org/TR/MathML2/dtd/xhtml-math11-f.dtd" [<!ENTITY mathml 'http://www.w3.org/1998/Math/MathML'>]>
   3 <html xmlns="http://www.w3.org/1999/xhtml">
   4 <head><title>hypergeometric6</title>
   5 <!-- MathML created with MathCast Equation Editor version 0.89 -->
   6 </head>
   7 <body>
   8 <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
   9   <mrow>
  10     <mtable columnalign="right center left">
  11       <mtr>
  12         <mtd>
  13           <mtext>mean</mtext>
  14         </mtd>
  15         <mtd>
  16           <mo>=</mo>
  17         </mtd>
  18         <mtd>
  19           <mfrac>
  20             <mrow>
  21               <mi>r</mi>
  22               <mi>n</mi>
  23             </mrow>
  24             <mi>N</mi>
  25           </mfrac>
  26         </mtd>
  27       </mtr>
  28       <mtr>
  29         <mtd>
  30           <mtext>mode</mtext>
  31         </mtd>
  32         <mtd>
  33           <mo>=</mo>
  34         </mtd>
  35         <mtd>
  36           <mtext>floor</mtext>
  37           <mfenced>
  38             <mrow>
  39               <mfrac>
  40                 <mrow>
  41                   <mfenced>
  42                     <mrow>
  43                       <mi>r</mi>
  44                       <mo>+</mo>
  45                       <mn>1</mn>
  46                     </mrow>
  47                   </mfenced>
  48                   <mfenced>
  49                     <mrow>
  50                       <mi>n</mi>
  51                       <mo>+</mo>
  52                       <mn>1</mn>
  53                     </mrow>
  54                   </mfenced>
  55                 </mrow>
  56                 <mrow>
  57                   <mi>N</mi>
  58                   <mo>+</mo>
  59                   <mn>2</mn>
  60                 </mrow>
  61               </mfrac>
  62             </mrow>
  63           </mfenced>
  64         </mtd>
  65       </mtr>
  66       <mtr>
  67         <mtd>
  68           <mtext>variance</mtext>
  69         </mtd>
  70         <mtd>
  71           <mo>=</mo>
  72         </mtd>
  73         <mtd>
  74           <mfrac>
  75             <mrow>
  76               <mi>r</mi>
  77               <mfenced>
  78                 <mrow>
  79                   <mfrac>
  80                     <mi>n</mi>
  81                     <mi>N</mi>
  82                   </mfrac>
  83                 </mrow>
  84               </mfenced>
  85               <mfenced>
  86                 <mrow>
  87                   <mn>1</mn>
  88                   <mo>&#x2212;</mo>
  89                   <mfrac>
  90                     <mi>n</mi>
  91                     <mi>N</mi>
  92                   </mfrac>
  93                 </mrow>
  94               </mfenced>
  95               <mfenced>
  96                 <mrow>
  97                   <mi>N</mi>
  98                   <mo>&#x2212;</mo>
  99                   <mi>r</mi>
 100                 </mrow>
 101               </mfenced>
 102             </mrow>
 103             <mfenced>
 104               <mrow>
 105                 <mi>N</mi>
 106                 <mo>&#x2212;</mo>
 107                 <mn>1</mn>
 108               </mrow>
 109             </mfenced>
 110           </mfrac>
 111         </mtd>
 112       </mtr>
 113       <mtr>
 114         <mtd>
 115           <mtext>skewness</mtext>
 116         </mtd>
 117         <mtd>
 118           <mo>=</mo>
 119         </mtd>
 120         <mtd>
 121           <mfrac>
 122             <mrow>
 123               <mfenced>
 124                 <mrow>
 125                   <mi>N</mi>
 126                   <mo>&#x2212;</mo>
 127                   <mn>2</mn>
 128                   <mi>n</mi>
 129                 </mrow>
 130               </mfenced>
 131               <msqrt>
 132                 <mfenced>
 133                   <mrow>
 134                     <mi>N</mi>
 135                     <mo>&#x2212;</mo>
 136                     <mn>1</mn>
 137                   </mrow>
 138                 </mfenced>
 139               </msqrt>
 140               <mfenced>
 141                 <mrow>
 142                   <mi>N</mi>
 143                   <mo>&#x2212;</mo>
 144                   <mn>2</mn>
 145                   <mi>r</mi>
 146                 </mrow>
 147               </mfenced>
 148             </mrow>
 149             <mrow>
 150               <msqrt>
 151                 <mrow>
 152                   <mi>r</mi>
 153                   <mi>n</mi>
 154                   <mfenced>
 155                     <mrow>
 156                       <mi>N</mi>
 157                       <mo>&#x2212;</mo>
 158                       <mi>n</mi>
 159                     </mrow>
 160                   </mfenced>
 161                   <mfenced>
 162                     <mrow>
 163                       <mi>N</mi>
 164                       <mo>&#x2212;</mo>
 165                       <mi>r</mi>
 166                     </mrow>
 167                   </mfenced>
 168                 </mrow>
 169               </msqrt>
 170               <mfenced>
 171                 <mrow>
 172                   <mi>N</mi>
 173                   <mo>&#x2212;</mo>
 174                   <mn>2</mn>
 175                 </mrow>
 176               </mfenced>
 177             </mrow>
 178           </mfrac>
 179         </mtd>
 180       </mtr>
 181       <mtr>
 182         <mtd>
 183           <mtext>kurtosis excess</mtext>
 184         </mtd>
 185         <mtd>
 186           <mo>=</mo>
 187         </mtd>
 188         <mtd>
 189           <mfenced>
 190             <mrow>
 191               <mfrac>
 192                 <mrow>
 193                   <msup>
 194                     <mi>N</mi>
 195                     <mn>2</mn>
 196                   </msup>
 197                   <mfenced>
 198                     <mrow>
 199                       <mi>N</mi>
 200                       <mo>&#x2212;</mo>
 201                       <mn>1</mn>
 202                     </mrow>
 203                   </mfenced>
 204                 </mrow>
 205                 <mrow>
 206                   <mi>r</mi>
 207                   <mfenced>
 208                     <mrow>
 209                       <mi>N</mi>
 210                       <mo>&#x2212;</mo>
 211                       <mn>2</mn>
 212                     </mrow>
 213                   </mfenced>
 214                   <mfenced>
 215                     <mrow>
 216                       <mi>N</mi>
 217                       <mo>&#x2212;</mo>
 218                       <mn>3</mn>
 219                     </mrow>
 220                   </mfenced>
 221                   <mfenced>
 222                     <mrow>
 223                       <mi>N</mi>
 224                       <mo>&#x2212;</mo>
 225                       <mi>r</mi>
 226                     </mrow>
 227                   </mfenced>
 228                 </mrow>
 229               </mfrac>
 230             </mrow>
 231           </mfenced>
 232           <mfenced>
 233             <mrow>
 234               <mfrac>
 235                 <mrow>
 236                   <mi>N</mi>
 237                   <mfenced>
 238                     <mrow>
 239                       <mi>N</mi>
 240                       <mo>+</mo>
 241                       <mn>1</mn>
 242                     </mrow>
 243                   </mfenced>
 244                   <mo>&#x2212;</mo>
 245                   <mn>6</mn>
 246                   <mi>N</mi>
 247                   <mfenced>
 248                     <mrow>
 249                       <mi>N</mi>
 250                       <mo>&#x2212;</mo>
 251                       <mi>r</mi>
 252                     </mrow>
 253                   </mfenced>
 254                 </mrow>
 255                 <mrow>
 256                   <mi>n</mi>
 257                   <mfenced>
 258                     <mrow>
 259                       <mi>N</mi>
 260                       <mo>&#x2212;</mo>
 261                       <mi>n</mi>
 262                     </mrow>
 263                   </mfenced>
 264                 </mrow>
 265               </mfrac>
 266               <mo>+</mo>
 267               <mfrac>
 268                 <mrow>
 269                   <mn>3</mn>
 270                   <mi>r</mi>
 271                   <mfenced>
 272                     <mrow>
 273                       <mi>N</mi>
 274                       <mo>&#x2212;</mo>
 275                       <mi>r</mi>
 276                     </mrow>
 277                   </mfenced>
 278                   <mfenced>
 279                     <mrow>
 280                       <mi>N</mi>
 281                       <mo>+</mo>
 282                       <mn>6</mn>
 283                     </mrow>
 284                   </mfenced>
 285                 </mrow>
 286                 <mrow>
 287                   <msup>
 288                     <mi>N</mi>
 289                     <mn>2</mn>
 290                   </msup>
 291                 </mrow>
 292               </mfrac>
 293               <mo>&#x2212;</mo>
 294               <mn>6</mn>
 295             </mrow>
 296           </mfenced>
 297         </mtd>
 298       </mtr>
 299     </mtable>
 300   </mrow>
 301 </math>
 302 </body>
 303 </html>