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Unit distributions, exhibiting inherent symmetrical properties, have been extensively studied across various fields. A significant challenge in these studies, particularly evident in parameter estimations, is the existence and uniqueness of estimators. Often, it is challenging to demonstrate the existence of a unique estimator. The major issue with maximum likelihood and other estimator-finding methods that use iterative methods is that they need an initial value to reach the solution. This dependency on initial values can lead to local extremes that fail to represent the global extremities, highlighting a lack of symmetry in solution robustness. This study applies a very simple, and unique, estimation method for unit Weibull and unit Burr XII distributions that both attain the global maximum value. Therefore, we can conclude that the findings from the obtained propositions demonstrate that both the maximum likelihood and graphical methods are symmetrically similar. In addition, three real-world data applications are made to show that the method works efficiently. [ABSTRACT FROM AUTHOR]

Unit distributions, exhibiting inherent symmetrical properties, have been extensively studied across various fields. A significant challenge in these studies, particularly evident in parameter estimations, is the existence and uniqueness of estimators. Often, it is challenging to demonstrate the existence of a unique estimator. The major issue with maximum likelihood and other estimator-finding methods that use iterative methods is that they need an initial value to reach the solution. This dependency on initial values can lead to local extremes that fail to represent the global extremities, highlighting a lack of symmetry in solution robustness. This study applies a very simple, and unique, estimation method for unit Weibull and unit Burr XII distributions that both attain the global maximum value. Therefore, we can conclude that the findings from the obtained propositions demonstrate that both the maximum likelihood and graphical methods are symmetrically similar. In addition, three real-world data applications are made to show that the method works efficiently.

In this paper, an investigation of the temporal rainfall variability in the South Island of New Zealand has been carried out using a high-quality monthly dataset of 152 rain gages with more than 50 years of observation. Possible trends in seasonal and annual rainfall values have been detected by means of the Mann–Kendall test and of a new graphical technique, Şen's method, which allows the trend identification of the low, medium, and high values of a series. As a result, different behaviors emerged in the South Island, with a rainfall increase in the southwest regions and a decrease in northeast areas. Moreover, the comparison of the trend methodologies has revealed different trend results (increasing, decreasing, or trendless time series). In particular, this study shows that Şen's method could be successfully used in the evaluation of peak and low values of data for the trend analysis of seasonal and annual rainfall values. [ABSTRACT FROM AUTHOR]

The design and evaluation of surface irrigation systems of a site requires reliable data of infiltration which could be provided by an infiltration model. In this study, Horton's infiltration model has been estimated for the soil located in a field of College of Agricultural Engineering and Technology, Dediapada, Gujarat using the infiltration data obtained from several locations in the field using double ring infiltrometer. The decay constant of the Horton's infiltration model was obtained using graphical method and also by using semi - log plot of t (time) vs. (f - fc), where f is the infiltration rate (mm/hr) and fc is the initial rate of infiltration capacity (mm/hr). The potential of the Horton's infiltration model so obtained was evaluated by least square fitting with the observed infiltration data. The Horton's infiltration model was used to estimate infiltration rate (mm/hr) and cumulative infiltration (cm). The Horton's model for infiltration rate obtained by semi-log plot method was obtained as i=20 + 94 e-1.02t, where i=infiltration rate (mm/hr) and t= time (min). The coefficient of determination obtained when the infiltration model was applied to observation data taken at various points in the field were found to 0.96. Therefore, it could be inferred that the Horton's infiltration model could give a reliable estimate of infiltration for the soil of Dediapada. [ABSTRACT FROM AUTHOR]

The two-parameter Weibull probability distribution function is versatile for modelling wind speed frequency distribution and for estimating the energy delivery potential of wind energy systems if its shape and scale parameters, k and c, are correctly determined from wind records. In this study, different methods for determining Weibull k and c from wind speed measurements are reviewed and applied at four sample meteorological stations in Zimbabwe. The appropriateness of each method in modelling the wind data is appraised by its accuracy in predicting the power density using relative deviation and normalised root mean square error. From the methods considered, the graphical method proved to imitate the wind data most closely followed by the standard deviation method. The Rayleigh distribution (k=2 is also generated and compared with the wind speed data. The Weibull parameters were calculated by the graphical method for fourteen stations at which hourly wind speed data was available. These values were then used, with the assistance of appropriate boundary layer models, in the mapping of a wind power density map at 50m hub height for Zimbabwe. [ABSTRACT FROM AUTHOR]

In this paper, a new life test plan called a progressively first-failure-censoring scheme introduced by Wu and Kuş [On estimation based on progressive first-failure-censored sampling, Comput. Statist. Data Anal. 53(10) (2009), pp. 3659–3670] is considered. Based on this type of censoring, the maximum likelihood (ML) and Bayes estimates for some survival time parameters namely reliability and hazard functions, as well as the parameters of the Burr-XII distribution are obtained. The Bayes estimators relative to both the symmetric and asymmetric loss functions are discussed. We use the conjugate prior for the one-shape parameter and discrete prior for the other parameter. Exact and approximate confidence intervals with the exact confidence region for the two-shape parameters are derived. A numerical example using the real data set is provided to illustrate the proposed estimation methods developed here. The ML and the different Bayes estimates are compared via a Monte Carlo simulation study. [ABSTRACT FROM PUBLISHER]