Algebra with random variables

• Probability density function (pdf)
  • Calculating the pdf from the cdf
    • ctx.pdf_from_cdf()
  • Calculating the pdf from the characteristic function
    • ctx.pdf_from_cf()
• Probability mass function (pmf)
  • Calculating the pmf from the cdf
    • ctx.pmf_from_cdf()
  • Calculating the pmf from the characteristic function
    • ctx.pmf_from_cf_lattice()
  • Calculating the pmf from the factorial moments
    • ctx.pmf_from_factorialmoments()
  • Approximating the pmf with asymptotic expansions
• Cumulative distribution function (cdf)
  • Calculating the cdf from the pdf
    • ctx.cdf_from_pdf()
  • Calculating the cdf from the pmf
    • ctx.cdf_from_pmf()
  • Calculating the cdf from the characteristic function
    • ctx.cdf_from_cf_continuous()
  • Calculating the cdf and sf from the characteristic function (lattice distribution)
    • ctx.cdf_from_cf_lattice()
  • Calculating the cdf from the factorial moments (lattice distributions)
• Quantile function
  • Calculating the quantile function from the cdf
  • Approximating the quantile function from the cumulant generating function
  • Approximating the quantile function from the cumulants
• Characteristic function
  • Calculating the characteristic function from the pdf (continuous distribution)
  • Calculating the characteristic function from the pmf (lattice distribution)
  • Calculating the characteristic function from the quantile function
  • Calculating the characteristic function from the raw moments
    • ctx.cf_from_rawmoments()
• Moment generating function
  • Calculating the moment-generating function from the pdf
    • ctx.mgf_from_pdf()
  • Calculating the moment-generating function from the characteristic function
    • ctx.mgf_from_cf()
  • Calculating the moment-generating function from the cumulant-generating function
    • ctx.mgf_from_cgf()
  • Calculating the moment-generating function from the probability-generating function
    • ctx.mgf_from_pgf()
  • Calculating the moment-generating function from the raw moments
    • ctx.mgf_from_rawmoments()
• Cumulant generating function
  • Calculating the cumulant-generating function from the characteristic function
    • ctx.cgf_from_cf()
  • Calculating the cumulant-generating function from the moment-generating function
    • ctx.cgf_from_mgf()
  • Calculating the cumulant-generating function from the probability-generating function
    • ctx.cgf_from_pgf()
  • Calculating the cumulant-generating function from the cumulants
    • ctx.cgf_from_cumulants()
• Probability generating function
  • Calculating the probability-generating function from the pmf vector
    • ctx.pgf_from_pmf_vector()
  • Calculating the probability-generating function from the moment-generating function
    • ctx.pgf_from_mgf()
• Factorial Moments
  • Calculating the factorial moments from the raw moments
    • ctx.factorial_moments_from_rawmoments()
  • Calculating the factorial moments from the cumulants
    • ctx.factorial_moments_from_cumulants()
• Raw Moments
  • Calculating the raw moments from the pdf
    • ctx.rawmoments_from_pdf()
  • Calculating the raw moments from the pmf
    • ctx.rawmoments_from_pmf_vector()
  • Calculating the raw moments from the factorial moments
    • ctx.rawmoments_from_factorial_moments()
  • Calculating the raw moments from the central moments
    • ctx.rawmoments_from_centralmoments()
  • Calculating the raw moments from the cumulants
    • ctx.rawmoments_from_cumulants()
  • Calculating the raw moments from the moment-generating function
    • ctx.rawmoments_from_mgf()
  • Calculating the raw moments from the characteristic function
    • ctx.rawmoments_from_cf()
  • Calculating the raw moments from the probability-generating function
    • ctx.rawmoments_from_pgf()
• Central Moments
  • Calculating the central moments from the factorial moments
    • ctx.centralmoments_from_factorialmoments()
  • Calculating the central moments from the raw moments
    • ctx.centralmoments_from_rawmoments()
  • Calculating the central moments from the cumulants
    • ctx.centralmoments_from_cumulants()
• Cumulants
  • Calculating the cumulants from the pmf vector
    • cumulants_from_pmfvector()
  • Calculating the cumulants from the factorial moments
    • ctx.cumulants_from_factorialmoments()
  • Calculating the cumulants from the raw moments
    • ctx.cumulants_from_rawmoments()
  • Calculating the cumulants from the central moments
    • ctx.cumulants_from_centralmoments()
  • Calculating the cumulants from the cumulant-generating function
    • ctx.cumulants_from_cdf()