Abstract: Scott (1985) proposed a frequency polygon density estimation,and proved that it dominated the histogram with respect to the criterionof integrated mean squared error and had the same rate of convergence to zero of the integrated mean squared error as non-negative kernel estimator for independent samples.For α mixing sequence,Carbon et al (1997) showed the uniformly strong consistency of the frequency polygons estimate and the convergence rate.Nadia and Sophie (2010) extended these results to the multivariate case.This paper extends the research to the case of the φ mixing samples,and proves theuniformly strong consistency of the frequency polygons estimate,which getsbetter convergent rate and weakens the conditions used by Carbon et al (1997) and Nadia and Sophie (2010).

Key words: frequency polygon density estimate, φ mixing sequence, strong consistency