A fair knowledge of the atmospheric muon distributions at Earth is a prerequisite for the simulations of cosmic ray setups and rare event search detectors. A modified power law is proposed for atmospheric muon energy distribution which gives a good description of the cosmic muon data in low as well as high energy regime. Using this distribution, analytical forms for zenith angle (θ) distribution are obtained. Assuming a flat Earth, it leads to the cos n−1 θ form where it is shown that the parameter n is nothing but the power of the energy distribution. Exact analytical function is obtained for inclined trajectory of muon. A new closed form for zenith angle distribution is obtained without assuming a flat Earth and which gives an improved description of the data at all angles even above 70 o . These distributions are tested with the available atmospheric muon data of energy and angular distributions. The parameters of these distributions can be used to characterize the cosmic muon data as a function of energy, angle and altitude.

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