Truncated models are imperative to efficiently analyze the finite data that we observe in almost all the real life situations. In this paper, a new truncated distribution having four parameters named Weibull-Truncated Exponential Distribution (W-TEXPD) is developed. The proposed model can be used as an alternative to the Exponential, standard Weibull and shifted Gamma-Weibull and three parameter Weibull distributions. The statistical characteristics including cumulative distribution function, hazard function, cumulative hazard function, central moments, skewness, kurtosis, percentile and entropy of the proposed model are derived. The maximum likelihood estimation method is employed to evaluate the unknown parameters of the W-TEXPD. A simulation study is also carried out to assess the performance of the model parameters. The proposed probability distribution is fitted on five data sets from different fields to demonstrate its vast application. A comparison of the proposed model with some extant models is given to justify the performance of the W-TEXPD.
The activity of fractions derived from hydroalcoholic extract of Dodonaea viscosa leaves against Candida albicans (Cl. I. 4043) was evaluated. The hydroalcoholic extract was sequentially fractionated to give n-hexane, dichloromethane, ethylacetate and n-butanol fractions that were subjected to qualitative phytochemical analyses. Disk diffusion assay was used in preliminary anticandidal screening with clotrimazole and chloroform serving as positive and negative controls, respectively. Optimized solvent systems were used for thin layer chromatography (TLC) that was followed by contact bioautography to evaluate the bioactivities of the fractions. Using broth microdilution technique, minimum inhibitory concentrations (MIC) of the individual fractions were established. With the exception of aqueous fraction all the fractions exhibited anticandidal activities (zone of inhibition 10 mm) in preliminary screening against test yeast. However, n-hexane fraction showed two inhibition zones at R f = 0.14 and 0.60 in contact bioautography, which indicates location of inhibitory compounds. The MIC of 62.5 µg/ml also supports the presence of anticandidal moieties in n-hexane fraction. Flavonoids, terpenoids, tannins and steroids were the main metabolites indicated in phytochemical screenings.
Traditionally, infinite models have been fitted on finite datasets which extrapolate the data, resulting in inadequate model fitting and predictions. To overcome this problem, we develop a new family of truncated distributions by introducing a new generator. In this article, a truncated random variable X t r “the transformer or input” is exerted to transform another random variable T “transformed or generator,” which yields a new T − X t r family of distributions. Several characteristics of T − X t r family of distributions are provided which are equally useful in engineering and biological sciences. For application purposes, a type-2 Gumbel-truncated exponential distribution is generated by using the proposed method along with its statistical properties. The efficacy of the new model is demonstrated by applying it to echophysiology and comparing the resulting outputs with those from the baseline models. Relevance of the Work. Indeed, the probability models have infinite domains but they are applied on the finite real datasets which may lead to exaggerated inferences and predictions. This problem can be solved by developing models that have finite domains. We propose finite models to analyze the finite data proficiently, provide reliable inferences, and save time.
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