V3-ProbabilityDistributionType.xml

**** MISSING DEFINITIONS ****

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      <p> Release Date: 2018-08-12</p> 

      <table class="grid">
 
        <tr> 
          <td> 
            <b> Level</b> 
          </td> 
          <td> 
            <b> Code</b> 
          </td> 
          <td> 
            <b> Display</b> 
          </td> 
          <td> 
            <b> Definition</b> 
          </td> 
        </tr> 
 
        <tr> 
          <td> 1</td> 
          <td> B
            <a name="v3-ProbabilityDistributionType-B"> </a> 
          </td> 
          <td> beta</td> 
          <td> 
                        The beta-distribution is used for data that is bounded on both
               sides and may or may not be skewed (e.g., occurs when probabilities are estimated.)  Two
               parameters a and b  are available to adjust the curve.  The mean m and variance s2 relate
               as follows: m = a/ (a + b) and s2 = ab/((a + b)2 (a + b + 1)).
            <br/>  

                     
          </td> 
        </tr> 
 
        <tr> 
          <td> 1</td> 
          <td> E
            <a name="v3-ProbabilityDistributionType-E"> </a> 
          </td> 
          <td> exponential</td> 
          <td> 
                        Used for data that describes extinction.  The exponential distribution
               is a special form of g-distribution where a = 1, hence, the relationship to mean m and
               variance s2 are m = b and s2 = b2.
            <br/>  

                     
          </td> 
        </tr> 
 
        <tr> 
          <td> 1</td> 
          <td> F
            <a name="v3-ProbabilityDistributionType-F"> </a> 
          </td> 
          <td> F</td> 
          <td> 
                        Used to describe the quotient of two c2 random variables.  The
               F-distribution has two parameters n1 and n2, which are the numbers of degrees of freedom
               of the numerator and denominator variable respectively. The relationship to mean m  and
               variance s2 are: m = n2 / (n2 - 2) and s2 = (2 n2 (n2 + n1 - 2)) / (n1 (n2 - 2)2 (n2 -
               4)).
            <br/>  

                     
          </td> 
        </tr> 
 
        <tr> 
          <td> 1</td> 
          <td> G
            <a name="v3-ProbabilityDistributionType-G"> </a> 
          </td> 
          <td> (gamma)</td> 
          <td> 
                        The gamma-distribution used for data that is skewed and bounded
               to the right, i.e. where the maximum of the distribution curve is located near the origin.
                The g-distribution has a two parameters a and b.  The relationship to mean m and variance
               s2 is m = a b and s2 = a b2.
            <br/>  

                     
          </td> 
        </tr> 
 
        <tr> 
          <td> 1</td> 
          <td> LN
            <a name="v3-ProbabilityDistributionType-LN"> </a> 
          </td> 
          <td> log-normal</td> 
          <td> 
                        The logarithmic normal distribution is used to transform skewed
               random variable X into a normally distributed random variable U = log X. The log-normal
               distribution can be specified with the properties mean m and standard deviation s.  Note
               however that mean m and standard deviation s are the parameters of the raw value distribution,
               not the transformed parameters of the lognormal distribution that are conventionally referred
               to by the same letters.  Those log-normal parameters mlog and slog relate to the mean
               m and standard deviation s of the data value through slog2 = log (s2/m2 + 1) and mlog
               = log m - slog2/2.
            <br/>  

                     
          </td> 
        </tr> 
 
        <tr> 
          <td> 1</td> 
          <td> N
            <a name="v3-ProbabilityDistributionType-N"> </a> 
          </td> 
          <td> normal (Gaussian)</td> 
          <td> 
                        This is the well-known bell-shaped normal distribution.  Because
               of the central limit theorem, the normal distribution is the distribution of choice for
               an unbounded random variable that is an outcome of a combination of many stochastic processes.
                Even for values bounded on a single side (i.e. greater than 0) the normal distribution
               may be accurate enough if the mean is &quot;far away&quot; from the bound of the scale
               measured in terms of standard deviations.
            <br/>  

                     
          </td> 
        </tr> 
 
        <tr> 
          <td> 1</td> 
          <td> T
            <a name="v3-ProbabilityDistributionType-T"> </a> 
          </td> 
          <td> T</td> 
          <td> 
                        Used to describe the quotient of a normal random variable and
               the square root of a c2 random variable.  The t-distribution has one parameter n, the
               number of degrees of freedom. The relationship to mean m  and variance s2 are: m = 0 and
               s2 = n / (n - 2)
            <br/>  

                     
          </td> 
        </tr> 
 
        <tr> 
          <td> 1</td> 
          <td> U
            <a name="v3-ProbabilityDistributionType-U"> </a> 
          </td> 
          <td> uniform</td> 
          <td> 
                        The uniform distribution assigns a constant probability over the
               entire interval of possible outcomes, while all outcomes outside this interval are assumed
               to have zero probability.  The width of this interval is 2s sqrt(3).  Thus, the uniform
               distribution assigns the probability densities f(x) = sqrt(2 s sqrt(3))  to values m -
               s sqrt(3) &gt;= x &lt;= m + s sqrt(3) and f(x) = 0 otherwise.
            <br/>  

                     
          </td> 
        </tr> 
 
        <tr> 
          <td> 1</td> 
          <td> X2
            <a name="v3-ProbabilityDistributionType-X2"> </a> 
          </td> 
          <td> chi square</td> 
          <td> 
                        Used to describe the sum of squares of random variables which
               occurs when a variance is estimated (rather than presumed) from the sample.  The only
               parameter of the c2-distribution is n, so called the number of degrees of freedom (which
               is the number of independent parts in the sum).  The c2-distribution is a special type
               of g-distribution with parameter a = n /2 and b  = 2.  Hence, m = n and s2 = 2 n.
            <br/>  

                     
          </td> 
        </tr> 

      </table> 

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  <title value="v3 Code System ProbabilityDistributionType"/> 
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  <date value="2018-08-12"/> 
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