Abstract Many issues in real life are riddled with confusion, vagueness, and ambiguity. The Topp-Leone distribution is a significant one-parameter probability distribution in the context of classical probability theory. There is a gap in the literature when it comes to dealing with circumstances involving interval-valued data with a classical Topp-Leone distribution. So, in this connection, neutrosophic Topp-Leone distribution is presented in this paper as an extension of the traditional Topp-Leone distribution. The new neutrosophic distribution takes into account the indeterminacy and crisp form of interval-valued distributions. The suggested distribution's mathematical features were derived, including moments and related measures, quantile function, survival, hazard, inverted hazard functions, and mills ratio. Maximum likelihood is used to estimate model parameters. Finally, a complex dataset is utilized to show the usefulness of the proposed distributions.
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