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<p>This paper introduces the Arcsin-New Cotangent (ANCT) family of distributions, a highly flexible lifetime model constructed by compounding an arcsine transformation with a cotangent-based mathematical framework. To demonstrate its practical utility, we extend the classical Weibull distribution to develop the three-parameter Arcsin-New Cotangent Weibull (ANCT-W) model. An explicit closed-form expression is derived for the quantile function to enable straightforward stochastic representation and data generation. Due to the analytical intractability of higher-order statistical properties under standard special functions, comprehensive numerical computations of key distributional characteristics—including the mean, variance, skewness, kurtosis, and quartiles—are performed across diverse parameter combinations via adaptive numerical routines. Parameter estimation is explored through six frequentist techniques alongside a Bayesian paradigm under a Markov Chain Monte Carlo framework. A comprehensive Monte Carlo simulation study across sample sizes ranging from <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(n=10\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>=</mo> <mn>10</mn> </mrow> </math></EquationSource> </InlineEquation> to <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(n=500\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>=</mo> <mn>500</mn> </mrow> </math></EquationSource> </InlineEquation> validates the global consistency of the estimators, showing a systematic decay of biases and mean squared errors toward zero as sample sizes grow. Finally, empirical justification of the competitive advantage of the ANCT-W model over well-known baseline alternatives is demonstrated through three real-world datasets: observed tensile strength of polyester fibers, mortality rates due to HIV/AIDS in Germany, and times to infection of kidney dialysis patients. Goodness-of-fit assessments confirm that the proposed framework yields a superior fit for engineering, public health, and survival data.</p>

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From Complexity to Applicability: The Arcsine New Cotangent Family of Distributions

  • 期刊论文

  • 发表日期：

    2026年7月27日

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  • Sadia Nadir,
  • Okechukwu J. Obulezi

摘要

This paper introduces the Arcsin-New Cotangent (ANCT) family of distributions, a highly flexible lifetime model constructed by compounding an arcsine transformation with a cotangent-based mathematical framework. To demonstrate its practical utility, we extend the classical Weibull distribution to develop the three-parameter Arcsin-New Cotangent Weibull (ANCT-W) model. An explicit closed-form expression is derived for the quantile function to enable straightforward stochastic representation and data generation. Due to the analytical intractability of higher-order statistical properties under standard special functions, comprehensive numerical computations of key distributional characteristics—including the mean, variance, skewness, kurtosis, and quartiles—are performed across diverse parameter combinations via adaptive numerical routines. Parameter estimation is explored through six frequentist techniques alongside a Bayesian paradigm under a Markov Chain Monte Carlo framework. A comprehensive Monte Carlo simulation study across sample sizes ranging from \(n=10\) n = 10 to \(n=500\) n = 500 validates the global consistency of the estimators, showing a systematic decay of biases and mean squared errors toward zero as sample sizes grow. Finally, empirical justification of the competitive advantage of the ANCT-W model over well-known baseline alternatives is demonstrated through three real-world datasets: observed tensile strength of polyester fibers, mortality rates due to HIV/AIDS in Germany, and times to infection of kidney dialysis patients. Goodness-of-fit assessments confirm that the proposed framework yields a superior fit for engineering, public health, and survival data.