FV_post_artan           Compute the final expected value of an
                        n-payment annuity, with payments of 1 unit each
                        made at the end of every year
                        (annuity-immediate), valued at the rate X,
                        using the tetraparametric function approach.
FV_post_beta_kmom       Compute the final expected value of an
                        n-payment annuity, with payments of 1 unit each
                        made at the end of every year
                        (annuity-immediate), valued at the rate X,
                        using the estimated moments of the beta
                        distribution.
FV_post_mood            Compute the final expected value of an
                        n-payment annuity, with payments of 1 unit each
                        made at the end of every year
                        (annuity-immediate), valued at the rate X,
                        using the method of Mood _et al._
FV_post_norm_kmom       Compute the final expected value of an
                        n-payment annuity, with payments of 1 unit each
                        made at the end of every year
                        (annuity-immediate), valued at the rate X,
                        using the estimated moments of the normal
                        distribution.
FV_post_quad            Compute the final expected value of an
                        n-payment annuity, with payments of 1 unit each
                        made at the end of every year
                        (annuity-immediate), valued at the rate X,
                        using the quadratic discount method.
FV_pre_artan            Compute the final expected value of an
                        n-payment annuity, with payments of 1 unit each
                        made at the beginning of every year
                        (annuity-due), valued at the rate X, using the
                        tetraparametric function approach.
FV_pre_beta_kmom        Compute the final expected value of an
                        n-payment annuity, with payments of 1 unit each
                        made at the beginning of every year
                        (annuity-due), valued at the rate X, using the
                        estimated moments of the beta distribution.
FV_pre_mood             Compute the final expected value of an
                        n-payment annuity, with payments of 1 unit each
                        made at the beginning of every year
                        (annuity-due), valued at the rate X, using the
                        method of Mood _et al._
FV_pre_norm_kmom        Compute the final expected value of an
                        n-payment annuity, with payments of 1 unit each
                        made at the beginning of every year
                        (annuity-due), valued at the rate X, using the
                        estimated moments of the normal distribution.
FV_pre_quad             Compute the final expected value of an
                        n-payment annuity, with payments of 1 unit each
                        made at the beginning of every year
                        (annuity-due), valued at the rate X, using the
                        quadratic discount method.
PV_post_artan           Compute present expected value of an n-payment
                        annuity, with payments of 1 unit each, made at
                        the end of every year (annuity-immediate),
                        valued at the rate X, using the tetraparametric
                        function approach.
PV_post_cubic           Compute the present expected value of an
                        n-payment annuity, with payments of 1 unit each
                        made at the end of every year (annuity-due),
                        valued at the rate X, using the cubic discount
                        method.
PV_post_exact           Computes the present value of an
                        annuity-immediate considering only non-central
                        moments of negative orders.
PV_post_mood_nm         Compute the present expected value of an
                        n-payment annuity, with payments of 1 unit each
                        made at the end of every year
                        (annuity-immediate), valued at the rate X, with
                        the method of Mood _et al._ using some negative
                        moments of the distribution.
PV_post_mood_pm         Compute the present expected value of an
                        n-payment annuity, with payments of 1 unit each
                        made at the end of every year
                        (annuity-immediate), valued at the rate X, with
                        the method of Mood _et al._ using some positive
                        moments of the distribution.
PV_post_triang_3        Compute the present value of an
                        annuity-immediate considering only non-central
                        moments of negative orders. The calculation is
                        performed by using the function
                        triangular\_moments\_3 for the moments greater
                        than -2 (in absolute value).
PV_post_triang_dis      Compute the present value of an
                        annuity-immediate considering only non-central
                        moments of negative orders. The calculation is
                        performed by using the moments of the fitted
                        triangular distribution of the random variable
                        "capitalization factor" U (which are obtained
                        from the definition of negative moment of a
                        continuous random variable).
PV_pre_artan            Compute the present expected value of an
                        n-payment annuity, with payments of 1 unit
                        each, made at the beginning of every year
                        (annuity-due), valued at the rate X, using the
                        tetraparametric function approach.
PV_pre_cubic            Compute the present expected value of an
                        n-payment annuity, with payments of 1 unit each
                        made at the beginning of every year
                        (annuity-due), valued at the rate X, using the
                        cubic discount method.
PV_pre_exact            Compute the present value of an annuity-due
                        considering only non-central moments of
                        negative orders.
PV_pre_mood_nm          Compute the present expected value of an
                        n-payment annuity, with payments of 1 unit each
                        made at the beginning of every year
                        (annuity-due), valued at the rate X, with the
                        method of Mood _et al._ using some negative
                        moments of the distribution.
PV_pre_mood_pm          Compute the present expected value of an
                        n-payment annuity, with payments of 1 unit each
                        made at the beginning of every year
                        (annuity-due), valued at the rate X, with the
                        method of Mood _et al._ using some positive
                        moments of the distribution.
PV_pre_triang_3         Compute the present value of an annuity-due
                        considering only non-central moments of
                        negative orders. The calculation is performed
                        by using the function $triangular\_moments\_3$
                        for the moments greater than -2 (in absolute
                        value).
PV_pre_triang_dis       Compute the present value of an annuity-due
                        considering only non-central moments of
                        negative orders. The calculation is performed
                        by using the moments of the fitted triangular
                        distribution of the random variable
                        "capitalization factor" U (which are obtained
                        from the definition of negative moment of a
                        continuous random variable)
beta_parameters         Compute the parameters of the beta distribution
                        and plot normalized data.
moment                  Compute the exact moments of a distribution.
norm_mom                Fit the data to a normal curve and compute the
                        moments of the normal distribution according to
                        the definition (as integral).
norm_test_jb            Compute the Jarque-Bera test for checking the
                        assumption of normality of the interest rates
                        distribution and returns the parameters of the
                        fitted normal distribution.
plot_FV_post_beta_kmom
                        Plot the final expected value of an n-payment
                        annuity, with payments of 1 unit each made at
                        the end of every year (annuity-immediate),
                        valued at the rate X, using the estimated
                        moments of the beta distribution.
plot_FV_post_norm_kmom
                        Plot the final expected value of an n-payment
                        annuity, with payments of 1 unit each made at
                        the end of every year (annuity-immediate),
                        valued at the rate X, using the estimated
                        moments of the normal distribution.
plot_FV_pre_beta_kmom   Plot the final expected value of an n-payment
                        annuity, with payments of 1 unit each made at
                        the beginning of every year (annuity-due),
                        valued at the rate X, using the estimated
                        moments of the beta distribution.
plot_FV_pre_norm_kmom   Plot the final expected value of an n-payment
                        annuity, with payments of 1 unit each made at
                        the beginning of every year (annuity-due),
                        valued at the rate X, using the estimated
                        moments of the normal distribution.
plot_FVs_post           Plot the final expected values of an n-payment
                        annuity, with payments of 1 unit each made at
                        the end of every year (annuity-immediate),
                        valued at the rate X, using different
                        approaches.
plot_FVs_pre            Plot the final expected values of an n-payment
                        annuity, with payments of 1 unit each made at
                        the beginning of every year (annuity-due),
                        valued at the rate X, using different
                        approaches.
plot_PVs_post           Plot the present expected values of an
                        n-payment annuity, with payments of 1 unit each
                        made at the end of every year
                        (annuity-immediate), valued at the rate X,
                        using different approaches.
plot_PVs_pre            Plot the present expected values of an
                        n-payment annuity, with payments of 1 unit each
                        made at the beginning of every year
                        (annuity-due), valued at the rate X, using
                        different approaches.
triangular_moments_3    Compute the negatives moments (different from
                        orders 1 and 2) of the fitted triangular
                        distribution of the random variable X.
triangular_moments_3_U
                        Compute the negatives moments (different from
                        orders 1 and 2) of the fitted triangular
                        distribution of the random variable
                        "capitalization factor" U.
triangular_moments_dis
                        Compute the negative moments of the fitted
                        triangular distribution of the random variable
                        X according to the definition (as integral).
triangular_moments_dis_U
                        Compute the negative moments of the fitted
                        triangular distribution of the random variable
                        "capitalization factor" U according to the
                        definition (as integral).
triangular_parameters   Compute the parameters and plot the fitted
                        triangular distribution of the random variable
                        X.
triangular_parameters_U
                        Return the parameters of the fitted triangular
                        distribution of the random variable
                        "capitalization factor" U.
variance_drv            Compute the variance of the present value of an
                        annuity using "discrete random variable"
                        approach.
variance_post_mood_nm   Compute the variance of the present value of an
                        annuity-immediate using the Mood _et al._
                        approximation and some non-central moments of
                        negative order.
variance_post_mood_pm   Compute the variance of the present value of an
                        annuity-immediate using the Mood _et al._
                        approximation and some non-central moments of
                        positive order.
variance_pre_mood_nm    Compute the variance of the present value of an
                        annuity-due using the Mood _et al._
                        approximation and some non-central moments of
                        negative order.
variance_pre_mood_pm    Compute the variance of the present value of an
                        annuity-due using the Mood _et al._
                        approximation and some non-central moments of
                        positive order.
