This paper proposes a stochastic method, ''mixed aleatory-epistemic“, for estimating solar PV hosting capacity (HC) of low-voltage (LV) distribution networks. The approach treats the aleatory and epistemic uncertainties in a different way. The HC is estimated by applying the transfer impedance matrix, 'which is only calculated once', and the superposition principle to determine the voltage magnitude rise due to solar PV. By distinguishing between aleatory and epistemic uncertainties, the calculations are limited to the relevant hours (time-of-day or time-of-year) during which high solar PV production is expected. In this way, the random aleatory uncertainties (background voltage, solar PV production, local consumption) are modelled by their probability distributions during the selected time period. The distributions for the epistemic uncertainties (installed capacity per customer, number of customers with solar PV, phase to which single-phase units are connected) are created with simple models involving the interval value and possible occurrence. The stochastic approach proposed is applied to three LV distribution networks to illustrate the method. The results show that both types of uncertainties affect the HC. The need for distribution network planners to identify and distinguish between the types of uncertainties is emphasised.