import math


def gumbel1(rp: int, xbar: float, std: float) -> float:
    """
    Solves the Gumbel Type 1 distribution
    Args:
        rp: return period (years)
        xbar: average of the dataset
        std: standard deviation of the dataset

    Returns:
        float: solution to gumbel distribution
    """
    return round(-math.log(-math.log(1 - (1 / rp))) * std * .7797 + xbar - (.45 * std), 3)