The TWIST collaboration has performed new measurements of two of the parameters that describe muon decay: $rho$, which governs the shape of the overall momentum spectrum, and $delta$, which governs the momentum dependence of the parity-violating decay asymmetry. This analysis gives the results $rho=0.75014pm 0.00017(text{stat})pm 0.00044(text{syst})pm 0.00011(eta)$, where the last uncertainty arises from the correlation between $rho$ and the decay parameter $eta$, and $delta = 0.75067pm 0.00030(text{stat})pm 0.00067(text{syst})$. These are consistent with the value of 3/4 given for both parameters in the Standard Model of particle physics, and are a factor of two more precise than the measurements previously published by TWIST. A new global analysis of all available muon decay data incorporating these results is presented. Improved lower and upper limits on the decay parameter $P_mu^pixi$ of $0.99524 < P_mu^pixi leq xi < 1.00091$ at 90% confidence are determined, where $P_mu^pi$ is the polarization of the muon when it is created during pion decay, and $xi$ governs the muon decay asymmetry. These results set new model-independent constraints on the possible weak interactions of right-handed particles. Specific implications for left-right symmetric models are discussed.
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