page_title: Bootstrapping populations
section_title: Algorithm
hierarchical_section_title: Bootstrapping populations / Algorithm
caption_attribution_description: English: Cumulative distribution function of the parameter A of a uniform continuous random variable
context_page_description: Starting with a sample observed from a random variable X having a given distribution law with a set of non fixed parameters which we denote with a vector, a parametric inference problem consists of computing suitable values – call them estimates – of these parameters precisely on the basis of the sample. An estimate is suitable if replacing it with the unknown parameter does not cause major damage in next computations. In Algorithmic inference, suitability of an estimate reads in terms of compatibility with the observed sample.
  In this framework, resampling methods are aimed at generating a set of candidate values to replace the unknown parameters that we read as compatible replicas of them. They represent a population of specifications of a random vector compatible with an observed sample, where the compatibility of its values has the properties of a probability distribution. By plugging parameters into the expression of the questioned distribution law, we bootstrap entire populations of random variables compatible with the observed sample.
context_section_description: You may easily see from a table of sufficient statistics that we obtain the curve in the picture on the left by computing the empirical distribution (2) on the population obtained through the above algorithm when: i) X is an Exponential random variable, ii) , and 
  ,
  and the curve in the picture on the right when: i)  X is a Uniform random variable in , ii) , and 
  .
caption: Cumulative distribution function of the parameter A of a uniform continuous random variable when statistic 
    
      
        
          
            s
            
              A
            
          
          =
          9.91
        
      
      {\displaystyle s_{A}=9.91}
exif: {}