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General two-parameter distribution: Statistical properties, estimation, and application on COVID-19.PloS One 2023In this paper, we introduced a novel general two-parameter statistical distribution which can be presented as a mix of both exponential and gamma distributions. Some...
In this paper, we introduced a novel general two-parameter statistical distribution which can be presented as a mix of both exponential and gamma distributions. Some statistical properties of the general model were derived mathematically. Many estimation methods studied the estimation of the proposed model parameters. A new statistical model was presented as a particular case of the general two-parameter model, which is used to study the performance of the different estimation methods with the randomly generated data sets. Finally, the COVID-19 data set was used to show the superiority of the particular case for fitting real-world data sets over other compared well-known models.
Topics: Humans; COVID-19; Models, Statistical; Statistical Distributions
PubMed: 36753497
DOI: 10.1371/journal.pone.0281474 -
Computational Intelligence and... 2022In this study, a new one-parameter count distribution is proposed by combining Poisson and XLindley distributions. Some of its statistical and reliability properties...
In this study, a new one-parameter count distribution is proposed by combining Poisson and XLindley distributions. Some of its statistical and reliability properties including order statistics, hazard rate function, reversed hazard rate function, mode, factorial moments, probability generating function, moment generating function, index of dispersion, Shannon entropy, Mills ratio, mean residual life function, and associated measures are investigated. All these properties can be expressed in explicit forms. It is found that the new probability mass function can be utilized to model positively skewed data with leptokurtic shape. Moreover, the new discrete distribution is considered a proper tool to model equi- and over-dispersed phenomena with increasing hazard rate function. The distribution parameter is estimated by different six estimation approaches, and the behavior of these methods is explored using the Monte Carlo simulation. Finally, two applications to real life are presented herein to illustrate the flexibility of the new model.
Topics: Computer Simulation; Likelihood Functions; Models, Statistical; Monte Carlo Method; Poisson Distribution; Reproducibility of Results; Statistical Distributions
PubMed: 35463286
DOI: 10.1155/2022/6503670 -
Cognition Oct 2022Humans can rapidly estimate the statistical properties of groups of stimuli, including their average and variability. But recent studies of so-called Feature...
Humans can rapidly estimate the statistical properties of groups of stimuli, including their average and variability. But recent studies of so-called Feature Distribution Learning (FDL) have shown that observers can quickly learn even more complex aspects of feature distributions. In FDL, observers learn the full shape of a distribution of features in a set of distractor stimuli and use this information to improve visual search: response times (RT) are slowed if the target feature lies inside the previous distractor distribution, and the RT patterns closely reflect the distribution shape. FDL requires only a few trials and is markedly sensitive to different distribution types. It is unknown, however, whether our perceptual system encodes feature distributions automatically and by passive exposure, or whether this learning requires active engagement with the stimuli. In two experiments, we sought to answer this question. During an initial exposure stage, participants passively viewed a display of 36 lines that included one orientation singleton or no singletons. In the following search display, they had to find an oddly oriented target. The orientations of the lines were determined either by a Gaussian or a uniform distribution. We found evidence for FDL only when the passive trials contained an orientation singleton. Under these conditions, RT's decreased as a function of the orientation distance between the target and the mean of the exposed distractor distribution. These results suggest that passive exposure to a distribution of visual features can affect subsequent search performance, but only if a singleton appears during exposure to the distribution.
Topics: Attention; Humans; Learning; Reaction Time; Statistical Distributions; Visual Perception
PubMed: 35785655
DOI: 10.1016/j.cognition.2022.105211 -
Computational Intelligence and... 2021In reliability studies, the best fitting of lifetime models leads to accurate estimates and predictions, especially when these models have nonmonotone hazard functions....
In reliability studies, the best fitting of lifetime models leads to accurate estimates and predictions, especially when these models have nonmonotone hazard functions. For this purpose, the new Exponential-X Fréchet (NEXF) distribution that belongs to the new exponential-X (NEX) family of distributions is proposed to be a superior fitting model for some reliability models with nonmonotone hazard functions and beat the competitive distribution such as the exponential distribution and Frechet distribution with two and three parameters. So, we concentrated our effort to introduce a new novel model. Throughout this research, we have studied the properties of its statistical measures of the NEXF distribution. The process of parameter estimation has been studied under a complete sample and Type-I censoring scheme. The numerical simulation is detailed to asses the proposed techniques of estimation. Finally, a Type-I censoring real-life application on leukaemia patient's survival with a new treatment has been studied to illustrate the estimation methods, which are well fitted by the NEXF distribution among all its competitors. We used for the fitting test the novel modified Kolmogorov-Smirnov (KS) algorithm for fitting Type-I censored data.
Topics: Computer Simulation; Humans; Leukemia; Models, Statistical; Reproducibility of Results; Statistical Distributions
PubMed: 34497637
DOI: 10.1155/2021/2167670 -
Journal of the Mechanical Behavior of... Feb 2024Aseptic loosening due to mechanical failure of bone cement is considered to be a leading cause of revision of joint replacement systems. Detailed quantified information...
Aseptic loosening due to mechanical failure of bone cement is considered to be a leading cause of revision of joint replacement systems. Detailed quantified information on the number, size and distribution pattern of pores can help to obtain a deeper understanding of the bone cement's fatigue behavior. The objective of this study was to provide statistical descriptions for the pore distribution characteristics of laboratory bone cement specimens with different amounts of antibiotic contents. For four groups of bone cement (Palacos) specimens, containing 0.3, 0.6, 1.2 and 2.4 wt/wt% of telavancin antibiotic, seven samples per group were micro computed tomography scanned (38.97 μm voxel size). The images were first preprocessed in Mimics and then analyzed in Dragonfly, with the level of threshold being set such that single-pixel pores become visible. The normalized pore volume data of the specimens were then used to extract the logarithmic histograms of the pore densities for antibiotic groups, as well as their three-parameter Weibull probability density functions. Statistical comparison of the pore distribution data of the antibiotic groups using the Mann-Whitney non-parametric test revealed a significantly larger porosity (p < 0.05) in groups with larger added antibiotic contents (2.4 and 0.6 wt/wt% vs 0.3 wt/wt%). Further analysis revealed that this effect was associated with the significantly larger frequency of micropores of 0.1-0.5 mm diameter (p < 0.05) in groups with larger antibiotic content (2.4 wt/wt% vs and 0.6 and 0.3 wt/wt%), implying that the elution of the added antibiotic produces micropores in this diameter range mainly. Based on this observation and the fatigue test results in the literature, it was suggested that micropore clusters have a detrimental effect on the mechanical properties of bone cement and play a major role in initiating fatigue cracks in highly antibiotic added specimens.
Topics: Animals; Polymethyl Methacrylate; Anti-Bacterial Agents; Bone Cements; Odonata; X-Ray Microtomography; Statistical Distributions
PubMed: 38100980
DOI: 10.1016/j.jmbbm.2023.106297 -
Biochemia Medica Feb 2020Uncertainty is an inseparable part of all types of measurement. Recently, the International Organization for Standardization (ISO) released a new standard (ISO 20914) on... (Review)
Review
Uncertainty is an inseparable part of all types of measurement. Recently, the International Organization for Standardization (ISO) released a new standard (ISO 20914) on how to calculate measurement uncertainty (MU) in laboratory medicine. This standard can be regarded as the beginning of a new era in laboratory medicine. Measurement uncertainty comprises various components and is used to calculate the total uncertainty. All components must be expressed in standard deviation (SD) and then combined. However, the characteristics of these components are not the same; some are expressed as SD, while others are expressed as a ± b, such as the purity of the reagents. All non-SD variables must be transformed into SD, which requires a detailed knowledge of common statistical distributions used in the calculation of MU. Here, the main statistical distributions used in MU calculation are briefly summarized.
Topics: Humans; Medical Laboratory Science; Statistical Distributions; Uncertainty
PubMed: 32063728
DOI: 10.11613/BM.2020.010101 -
Journal of Theoretical Biology Oct 2016Sequence comparison has become an essential tool in bioinformatics, because highly homologous sequences usually imply significant functional or structural similarity.... (Comparative Study)
Comparative Study
Sequence comparison has become an essential tool in bioinformatics, because highly homologous sequences usually imply significant functional or structural similarity. Traditional sequence analysis techniques are based on preprocessing and alignment, which facilitate measuring and quantitative characterization of genetic differences, variability and complexity. However, recent developments of next generation and whole genome sequencing technologies give rise to new challenges that are related to measuring similarity and capturing rearrangements of large segments contained in the genome. This work is devoted to illustrating different methods recently introduced for quantifying sequence distances and variability. Most of the alignment-free methods rely on counting words, which are small contiguous fragments of the genome. Our approach considers the locations of nucleotides in the sequences and relies more on appropriate statistical distributions. The results of this technique for comparing sequences, by extracting information and comparing matching fidelity and location regularization information, are very encouraging, specifically to classify mutation sequences.
Topics: Algorithms; Base Sequence; Cluster Analysis; Genome; Genome, Bacterial; Genome, Mitochondrial; Genomics; Herpesviridae; Mutation; Phylogeny; Statistical Distributions
PubMed: 27460589
DOI: 10.1016/j.jtbi.2016.07.032 -
Studies in Health Technology and... Jun 2022We compared the distribution of laboratory test values with several parametric statistical distributions to show that a lognormal distribution can represent the...
We compared the distribution of laboratory test values with several parametric statistical distributions to show that a lognormal distribution can represent the distribution of laboratory test values. Then, we estimated the distributions of laboratory test values of four datasets including only three published values: two endpoints of reference interval (RI) and one median.
Topics: Reference Values; Statistical Distributions
PubMed: 35673208
DOI: 10.3233/SHTI220270 -
Acta Ophthalmologica 1965
Topics: Eye Diseases; Glaucoma; Humans; Intraocular Pressure; Statistical Distributions; Statistics as Topic; Tonometry, Ocular
PubMed: 14293654
DOI: 10.1111/j.1755-3768.1965.tb05455.x -
IEEE Transactions on Bio-medical... Nov 2006The recent papers by Miranda de Sa et al. (2001) and Miranda de Sa (2004) proposed a new measure of coherence between two signals. In this paper, we derive the exact...
The recent papers by Miranda de Sa et al. (2001) and Miranda de Sa (2004) proposed a new measure of coherence between two signals. In this paper, we derive the exact probability density function and moments of the measure. We also provide simple programs for computing the associated cumulative distribution function and percentile points as well as for generating random samples of the measure.
Topics: Adolescent; Algorithms; Child; Computer Simulation; Cortical Synchronization; Data Interpretation, Statistical; Electroencephalography; Humans; Models, Neurological; Models, Statistical; Monte Carlo Method; Photic Stimulation; Regression Analysis; Signal Processing, Computer-Assisted; Statistical Distributions
PubMed: 17073349
DOI: 10.1109/TBME.2006.883625