Definition for Value SetProbabilityDistributionType

<?xml version="1.0" encoding="UTF-8"?>

<ValueSet xmlns="http://hl7.org/fhir">
  <id value="probability-distribution-type"/> 
  <meta> 
    <lastUpdated value="2023-03-01T23:03:57.298+11:00"/> 
    <profile value="http://hl7.org/fhir/StructureDefinition/shareablevalueset"/> 
  </meta> 
  <text> 
    <status value="extensions"/> 
    <div xmlns="http://www.w3.org/1999/xhtml">
      <ul> 
        <li> Include these codes as defined in 
          <a href="http://terminology.hl7.org/4.0.0/CodeSystem-v3-ProbabilityDistributionType.html">
            <code> http://terminology.hl7.org/CodeSystem/v3-ProbabilityDistributionType</code> 
          </a> 
          <table class="none">
            <tr> 
              <td style="white-space:nowrap">
                <b> Code</b> 
              </td> 
              <td> 
                <b> Display</b> 
              </td> 
              <td> 
                <b> Definition</b> 
              </td> 
            </tr> 
            <tr> 
              <td> 
                <a href="http://terminology.hl7.org/4.0.0/CodeSystem-v3-ProbabilityDistributionType.html#v3-Probabilit
                yDistributionType-B">B</a> 
              </td> 
              <td> beta</td> 
              <td> The beta-distribution is used for data that is bounded on both sides and might
                 or might 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)).</td> 
            </tr> 
            <tr> 
              <td> 
                <a href="http://terminology.hl7.org/4.0.0/CodeSystem-v3-ProbabilityDistributionType.html#v3-Probabilit
                yDistributionType-E">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.</td> 
            </tr> 
            <tr> 
              <td> 
                <a href="http://terminology.hl7.org/4.0.0/CodeSystem-v3-ProbabilityDistributionType.html#v3-Probabilit
                yDistributionType-F">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)).</td> 
            </tr> 
            <tr> 
              <td> 
                <a href="http://terminology.hl7.org/4.0.0/CodeSystem-v3-ProbabilityDistributionType.html#v3-Probabilit
                yDistributionType-G">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.</td> 
            </tr> 
            <tr> 
              <td> 
                <a href="http://terminology.hl7.org/4.0.0/CodeSystem-v3-ProbabilityDistributionType.html#v3-Probabilit
                yDistributionType-LN">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.</td> 
            </tr> 
            <tr> 
              <td> 
                <a href="http://terminology.hl7.org/4.0.0/CodeSystem-v3-ProbabilityDistributionType.html#v3-Probabilit
                yDistributionType-N">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.</td> 
            </tr> 
            <tr> 
              <td> 
                <a href="http://terminology.hl7.org/4.0.0/CodeSystem-v3-ProbabilityDistributionType.html#v3-Probabilit
                yDistributionType-T">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)</td> 
            </tr> 
            <tr> 
              <td> 
                <a href="http://terminology.hl7.org/4.0.0/CodeSystem-v3-ProbabilityDistributionType.html#v3-Probabilit
                yDistributionType-U">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.</td> 
            </tr> 
            <tr> 
              <td> 
                <a href="http://terminology.hl7.org/4.0.0/CodeSystem-v3-ProbabilityDistributionType.html#v3-Probabilit
                yDistributionType-X2">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.</td> 
            </tr> 
          </table> 
        </li> 
      </ul> 
    </div> 
  </text> 
  <extension url="http://hl7.org/fhir/StructureDefinition/structuredefinition-wg">
    <valueCode value="fhir"/> 
  </extension> 
  <url value="http://hl7.org/fhir/ValueSet/probability-distribution-type"/> 
  <identifier> 
    <system value="urn:ietf:rfc:3986"/> 
    <value value="urn:oid:2.16.840.1.113883.4.642.3.907"/> 
  </identifier> 
  <version value="5.0.0-draft-final"/> 
  <name value="ProbabilityDistributionType"/> 
  <title value="ProbabilityDistributionType"/> 
  <status value="draft"/> 
  <experimental value="false"/> 
  <date value="2023-03-01T23:03:57+11:00"/> 
  <publisher value="HL7 (FHIR Project)"/> 
  <contact> 
    <telecom> 
      <system value="url"/> 
      <value value="http://hl7.org/fhir"/> 
    </telecom> 
    <telecom> 
      <system value="email"/> 
      <value value="fhir@lists.hl7.org"/> 
    </telecom> 
  </contact> 
  <description value="Codes specifying the type of probability distribution."/> 
  <jurisdiction> 
    <coding> 
      <system value="http://unstats.un.org/unsd/methods/m49/m49.htm"/> 
      <code value="001"/> 
      <display value="World"/> 
    </coding> 
  </jurisdiction> 
  <compose> 
    <include> 
      <system value="http://terminology.hl7.org/CodeSystem/v3-ProbabilityDistributionType"/> 
      <concept> 
        <extension url="http://hl7.org/fhir/StructureDefinition/valueset-concept-definition">
          <valueString value="The beta-distribution is used for data that is bounded on both sides and might
           or might 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))."/> 
        </extension> 
        <code value="B"/> 
        <display value="beta"/> 
      </concept> 
      <concept> 
        <extension url="http://hl7.org/fhir/StructureDefinition/valueset-concept-definition">
          <valueString value="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."/> 
        </extension> 
        <code value="E"/> 
        <display value="exponential"/> 
      </concept> 
      <concept> 
        <extension url="http://hl7.org/fhir/StructureDefinition/valueset-concept-definition">
          <valueString value="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))."/> 
        </extension> 
        <code value="F"/> 
        <display value="F"/> 
      </concept> 
      <concept> 
        <extension url="http://hl7.org/fhir/StructureDefinition/valueset-concept-definition">
          <valueString value="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."/> 
        </extension> 
        <code value="G"/> 
        <display value="(gamma)"/> 
      </concept> 
      <concept> 
        <extension url="http://hl7.org/fhir/StructureDefinition/valueset-concept-definition">
          <valueString value="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."/> 
        </extension> 
        <code value="LN"/> 
        <display value="log-normal"/> 
      </concept> 
      <concept> 
        <extension url="http://hl7.org/fhir/StructureDefinition/valueset-concept-definition">
          <valueString value="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."/> 
        </extension> 
        <code value="N"/> 
        <display value="normal (Gaussian)"/> 
      </concept> 
      <concept> 
        <extension url="http://hl7.org/fhir/StructureDefinition/valueset-concept-definition">
          <valueString value="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)"/> 
        </extension> 
        <code value="T"/> 
        <display value="T"/> 
      </concept> 
      <concept> 
        <extension url="http://hl7.org/fhir/StructureDefinition/valueset-concept-definition">
          <valueString value="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."/> 
        </extension> 
        <code value="U"/> 
        <display value="uniform"/> 
      </concept> 
      <concept> 
        <extension url="http://hl7.org/fhir/StructureDefinition/valueset-concept-definition">
          <valueString value="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."/> 
        </extension> 
        <code value="X2"/> 
        <display value="chi square"/> 
      </concept> 
    </include> 
  </compose> 
</ValueSet>