Upper/lower bound and initial domain for lognormal distribution

Question

I'm trying to implement logNormal distribution into my java program because lognormal dist doesn't exist into apache commons math library.

I have no problem to re-write density and cumulative probability function, extending abstract classes of apache commons math library, like this :

 public double cumulativeProbability(double mu, double sigma, double x) {

        if (sigma <= 0.0) {
            throw new IllegalArgumentException("sigma  <= 0");
        }
        if (x <= 0.0) {
            return 0.0;
        }

        return this.cumulativeProbability((Math.log(x) - mu) / sigma);
    }

 public double cumulativeProbability(double x){

        double var = 0.0;
        NormalDistributionImpl normalDist = new NormalDistributionImpl();

        try {
            var = normalDist.cumulativeProbability(x);
        } catch (MathException e) {}

        return var;  
    }


  public double density (double x) {
      return density (mu, sigma, x);
  }


  public static double density (double mu, double sigma, double x) {

      if (sigma <= 0)
         throw new IllegalArgumentException ("sigma <= 0");
      if (x <= 0)
         return 0;
      double diff = Math.log (x) - mu;
      return Math.exp (-diff*diff/(2*sigma*sigma))/
              (Math.sqrt (2*Math.PI)*sigma*x);
   }

Apache commons math need implementation of a list of utilies function to compute the inverse cumulative probability, and i don't know which upper/lowerbound/initial domain my lognormal distribution can take ...

I suppose it's something like this, but i'm not sure : x between [0 ; +infinity] ?

Thanks a lot for your help

---

p = Desired probability for the critical value.

Access the domain value lower bound, based on p, used to bracket a CDF root. This method is used by inverseCumulativeProbability(double) to find critical values.

  public double getDomainLowerBound(double p){
    return ?;
  }

Access the domain value upper bound, based on p, used to bracket a CDF root. This method is used by inverseCumulativeProbability(double) to find critical values.

  public double getDomainUpperBound(double p){
    return ?;
  }

Access the initial domain value, based on p, used to bracket a CDF root. This method is used by inverseCumulativeProbability(double) to find critical values.

  public double getInitialDomain(double p){
    return ?;
  }

Access the lower bound of the support. Returns: lower bound of the support (might be Double.NEGATIVE_INFINITY)

  public double getSupportLowerBound(){
    return ?;
  }

Access the upper bound of the support. Returns: upper bound of the support (might be Double.POSITIVE_INFINITY)

  public double getSupportUpperBound(){
    return ?;
  }

Use this method to get information about whether the lower bound of the support is inclusive or not. Returns: whether the lower bound of the support is inclusive or not

  public  boolean isSupportLowerBoundInclusive(){
      return ;
  }

Use this method to get information about whether the upper bound of the support is inclusive or not. Returns: whether the upper bound of the support is inclusive or not

  public boolean isSupportUpperBoundInclusive(){
      return ;
  }

Answer 1

The support for the log normal distribution is the open interval from 0 to infinity. This should give you enough information to implement all methods that have 'Bound' in their name.

I understand that the methods with 'Domain' in their name are used to provide bounds and estimates for the inverse CDF that are easy to compute; for this you can easily follow @whuber's suggestion and return the $\exp$ of the corresponding values for the normal distribution. It's instructive to see what the implementors use for that: if $p \not= \frac{1}{2}$, then the infinite interval on the appropriate side of $\mu$ provides the bounds and the initial estimate is $\mu \pm \sigma$. So you could also directly return the $\exp$ of these values.