def alpha_beta_max_to_mu_chi_var_chi_max(alpha, beta, amax):
    """
    Convert between parameters for beta distribution
    """
    mu_chi = alpha / (alpha + beta) * amax
    var_chi = alpha * beta / ((alpha + beta)**2 * (alpha + beta + 1)) * amax**2
    return mu_chi, var_chi, amax