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In this article, we introduce and study the truncated inverse power Lindley distribution. The aim is to transpose the remarkable flexibility of the two-parameter inverse power Lindley distribution to the interval [0,1]. The corresponding probability density function has the potential to be unimodal, decreasing, right-skewed, and heavy-tailed. On the other hand, the hazard rate function can be increasing, N-shaped, or U-shaped. These shapes’ versatility enables accurate representation and analysis of proportional or percentage data across a wide range of applications, such as survival analysis, reliability, and uncertainty modeling. Several statistical features, such as the mode, quantiles, Bowley’s skewness, Moor’s kurtosis, MacGillivray’s skewness, moments, inverse moments, incomplete moments, and probability-weighted moments, are computed. In practice, for the estimation of the model parameters from truncated data under the progressively type-II censoring scheme, the maximum likelihood, maximum product spacing, and Bayesian approaches are used. The Tierney–Kadane approximation and Markov chain Monte Carlo techniques are employed to produce the Bayesian estimates under the squared error loss function. We present some simulation results to evaluate these approaches. Four applications based on real-world datasets—one of them is on times of infection, the second is on failure times, and the other two are on the rate of inflation in Asia and Africa—explain the significance of the new truncated model in comparison to some reputed comparable models, such as the inverse power Lindley, Kumaraswamy, truncated power Lomax, beta, truncated Weibull, unit-Weibull, Kumaraswamy Kumaraswamy, and exponentiated Kumaraswamy models.
In this article, we introduce and study the truncated inverse power Lindley distribution. The aim is to transpose the remarkable flexibility of the two-parameter inverse power Lindley distribution to the interval [0,1]. The corresponding probability density function has the potential to be unimodal, decreasing, right-skewed, and heavy-tailed. On the other hand, the hazard rate function can be increasing, N-shaped, or U-shaped. These shapes’ versatility enables accurate representation and analysis of proportional or percentage data across a wide range of applications, such as survival analysis, reliability, and uncertainty modeling. Several statistical features, such as the mode, quantiles, Bowley’s skewness, Moor’s kurtosis, MacGillivray’s skewness, moments, inverse moments, incomplete moments, and probability-weighted moments, are computed. In practice, for the estimation of the model parameters from truncated data under the progressively type-II censoring scheme, the maximum likelihood, maximum product spacing, and Bayesian approaches are used. The Tierney–Kadane approximation and Markov chain Monte Carlo techniques are employed to produce the Bayesian estimates under the squared error loss function. We present some simulation results to evaluate these approaches. Four applications based on real-world datasets—one of them is on times of infection, the second is on failure times, and the other two are on the rate of inflation in Asia and Africa—explain the significance of the new truncated model in comparison to some reputed comparable models, such as the inverse power Lindley, Kumaraswamy, truncated power Lomax, beta, truncated Weibull, unit-Weibull, Kumaraswamy Kumaraswamy, and exponentiated Kumaraswamy models.
In this study, we suggest the truncated version of the inverse power Ailamujia distribution, which is more flexible than other well-known distributions. Statistical properties of the new distribution are considered, such as moments, moment generating function, incomplete moments, quantile function, order statistics, and entropy. We discuss various methods of estimation, such as the method of maximum likelihood, methods of least squares and weighted least squares, the method of the maximum product of spacings, the method of Cramer and Von-Mises, methods of Anderson and Darling and right-tail Anderson and Darling, the method of percentiles, and the Bayesian method. Simulation is implemented to study the performance of estimates. We introduce two real data applications, showing that the new distribution can provide better fits than some other corresponding distributions.
Statistical distributions have great applicability for modeling data in almost every applied sector. Among the available classical distributions, the inverse Weibull distribution has received considerable attention. In the practice of distribution theory, numerous methods have been studied and suggested/introduced to increase the flexibility level of the traditional probability distributions. In this paper, we implement different distribution methods to obtain five new different versions of the inverse Weibull model. The new modifications of the inverse Weibull model are called the logarithm transformed-inverse Weibull, a flexible reduced logarithmic-inverse Weibull, the weighted TX-inverse Weibull, a new generalized-inverse Weibull, and the alpha power transformed extended-inverse Weibull distributions. To illustrate the flexibility and applicability of the new modifications of the inverse Weibull model, a biomedical data set is analyzed. The data set consists of 108 observations and represents the mortality rate of the COVID-19-infected patients. The practical application shows that the new generalized-inverse Weibull is the best modification of the inverse Weibull distribution.
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