We study the rate of convergence for the renewal density with the interarrival times that are absolutely continuous, not necessarily positive, and has finite moment of $\alpha$th order with $\alpha$ > 3/2. We obtain an error estimate that is better than known results. Our method is based on modification of functions that have the same tails as the original ones and have integrable Fourier transform.
"Fractional order error estimates for the renewal density." J. Math. Soc. Japan 68 (1) 31 - 49, January, 2016. https://doi.org/10.2969/jmsj/06810031