In this paper, we establish the links between the H\"older and Lehmer central tendencies and the maximum likelihood for the estimation of the one-parameter exponential family of probability density functions. For this, we show that the maximum weighted likelihood of the parameter is a generalized weighted mean from which the central tendencies of H\"older and Lehmer can be inferred. Some of the links obtained do not seem to be part of the state of the art. Moreover, we show that the maximum weighted likelihood is equivalent to the minimum of the weighted least square error. Experimentations confirm that the maximum weighted likelihood leads to a more accurate fitting of histograms.

翻译：本文建立了Hölder与Lehmer中心趋势同单参数指数族概率密度函数最大似然估计之间的联系。为此，我们证明了参数的最大加权似然估计是一种广义加权均值，由此可推导出Hölder与Lehmer中心趋势。所获得的某些联系似乎不属于现有技术范畴。此外，我们还证明了最大加权似然性等价于加权最小二乘误差的最小化。实验证实，最大加权似然性能够更精确地拟合直方图。