Lognormal Model Research Articles

Selection on early survival does not explain germination rate clines in Mimulus cardinalis.

Many traits covary with environmental gradients to form phenotypic clines. While local adaptation to the environment can generate phenotypic clines, other nonadaptive processes may also. If local adaptation causes phenotypic clines, then the direction of genotypic selection on traits should shift from one end of the cline to the other. Traditionally, genotypic selection on non-Gaussian traits like germination rate have been hampered because it is challenging to measure their genetic variance. Here we used quantitative genetics and reciprocal transplants to test whether a previously discovered cline in germination rate showed additional signatures of adaptation in the scarlet monkeyflower (Mimulus cardinalis). We measured genotypic and population level covariation between germination rate and early survival, a component of fitness. We developed a novel discrete log-normal model to estimate genetic variance in germination rate. Contrary to our adaptive hypothesis, we found no evidence that genetic variation in germination rate contributed to variation in early survival. Across populations, southern populations in both gardens germinated earlier and survived more. Southern populations have higher early survival but it is not caused by faster germination. This pattern is consistent with nonadaptive forces driving the phenotypic cline in germination rate, but future work will need to assess whether there is selection at other life stages. This statistical framework should help expand quantitative genetic analyses for other waiting-time traits.

Exploring short-term optical variability of blazars using TESS

ABSTRACT We present a first systematic time series study of a sample of blazars observed by the Transiting Exoplanet Survey Satellite (TESS). By cross matching the positions of the sources in the TESS observations with those from Roma-BZCAT, 29 blazars including both BL Lacerate objects and flat-spectrum radio quasars were identified. The observation lengths of the 79 light curves of the sources, across all sectors on which the targets of interest have been observed by TESS, range between 21.25 and 28.2 d. The light curves were analysed using various methods of time series analysis. The results show that the sources exhibit significant variability with fractional variability spanning between 1.41 per cent and 53.84 per cent. The blazar flux distributions were studied by applying normal and log-normal probability density function models. The results indicate that optical flux histogram of the sources are consistent with normal probability density function with most of them following bimodal distribution as opposed to unimodal distribution. This suggests that the days-time-scale optical variability is contributed either by two different emission zones or two distinct states of short-term activity in blazars. Power spectral density analysis was performed by using the power spectral response method and the true power spectra of unevenly sampled light curves were estimated. The power spectral slopes of the light curves ranged from 1.7 to 3.2.

Limitations of the Wasserstein MDE for univariate data

Minimum Kolmogorov and Wasserstein distance estimates, hat{theta }_{MKD} and hat{theta }_{MWD}, respectively, of model parameter, theta (in Theta ), are empirically compared, obtained assuming the model is intractable. For the Cauchy and Lognormal models, simulations indicate both estimates have expected values nearly theta , but hat{theta }_{MKD} has in all repetitions of the experiments smaller SD than hat{theta }_{MWD}, and hat{theta }_{MKD}’s relative efficiency with respect to hat{theta }_{MWD} improves as the sample size, n, increases. The minimum expected Kolmogorov distance estimate, hat{theta }_{MEKD}, has eventually bias and SD both smaller than the corresponding Wasserstein estimate, hat{theta }_{MEWD}, and hat{theta }_{MEKD}’s relative efficiency improves as n increases. These results hold also for stable models with stability index alpha =.5 and alpha =1.1. For the Uniform and the Normal models the estimates have similar performance. The disturbing empirical findings for hat{theta }_{MWD} are due to the unboudedness and non-robustness of the Wasserstein distance and the heavy tails of the underlying univariate models.Theoretical confirmation is provided for stable models with 1<alpha <2, which have finite first moment. Similar results are expected to hold for multivariate heavy tail models. Combined with existing results in the literature, the findings do not support the use of Wasserstein distance in statistical inference, especially for intractable and Black Box models with unverifiable heavy tails.

A bayesian approach to model the underlying predictors of early recurrence and postoperative death in patients with colorectal Cancer

ObjectiveThis study aimed at utilizing a Bayesian approach semi-competing risks technique to model the underlying predictors of early recurrence and postoperative Death in patients with colorectal cancer (CRC).MethodsIn this prospective cohort study, 284 patients with colorectal cancer, who underwent surgery, referred to Imam Khomeini clinic in Hamadan from 2001 to 2017. The primary outcomes were the probability of recurrence, the probability of Mortality without recurrence, and the probability of Mortality after recurrence. The patients ‘recurrence status was determined from patients’ records. The Bayesian survival modeling was carried out by semi-competing risks illness-death models, with accelerated failure time (AFT) approach, in R 4.1 software. The best model was chosen according to the lowest deviance information criterion (DIC) and highest logarithm of the pseudo marginal likelihood (LPML).ResultsThe log-normal model (DIC = 1633, LPML = -811), was the optimal model. The results showed that gender(Time Ratio = 0.764: 95% Confidence Interval = 0.456–0.855), age at diagnosis (0.764: 0.538–0.935 ), T3 stage (0601: 0.530–0.713), N2 stage (0.714: 0.577–0.935 ), tumor size (0.709: 0.610–0.929), grade of differentiation at poor (0.856: 0.733–0.988), and moderate (0.648: 0.503–0.955) levels, and the number of chemotherapies (1.583: 1.367–1.863) were significantly related to recurrence. Also, age at diagnosis (0.396: 0.313–0.532), metastasis to other sites (0.566: 0.490–0.835), T3 stage (0.363: 0.592 − 0.301), T4 stage (0.434: 0.347–0.545), grade of differentiation at moderate level (0.527: 0.387–0.674), tumor size (0.595: 0.500–0.679), and the number of chemotherapies (1.541: 1.332–2.243) were the significantly predicted the death. Also, age at diagnosis (0.659: 0.559–0.803), and the number of chemotherapies (2.029: 1.792–2.191) were significantly related to mortality after recurrence.ConclusionAccording to specific results obtained from the optimal Bayesian log-normal model for terminal and non-terminal events, appropriate screening strategies and the earlier detection of CRC leads to substantial improvements in the survival of patients.

Species-Abundance Distribution Patterns of Plant Communities in the Gurbantünggüt Desert, China

It is important to study the species-abundance distribution pattern in a community to reveal the mechanism of community assembly. Six abundance models (log-normal distribution model, Zipf model, Zipf–Mandelbrot model, broken stick model, niche preemption model, and Volkov model) were used to fit the species-abundance distribution pattern of six scales (10 m × 10 m, 20 m × 20 m, 40 m ×40 m, 60 m × 60 m, 80 m × 80 m, 100 m × 100 m) in fixed, semifixed, and mobile sand dunes in the Gurbantünggüt Desert, respectively. The best-fitting model was determined using the K-S test, the Chi-square test, and the Akaike information criterion. The results showed that the values of soil salinity, nutrients, water content, Shannon–Wiener diversity index (H′), Pielou evenness index (E), and Simpson index (D) were ranked in all three habitats as fixed dunes &gt; semifixed dunes &gt; mobile dunes. The rank curves span a narrow range on the horizontal axis at scales of 10 m × 10 m and 20 m × 20 m, and species richness is minimal. As the scale increases, the span range of the curve gradually increases, and species richness becomes higher at scales of 40 m × 40 m, 60 m × 60 m, 80 m × 80 m, and 100 m × 100 m. At the 10 m × 10 m and 20 m × 20 m scales, the broken stick model fits best in the three dune habitats. At the 40 m × 40 m and 60 m × 60 m scales, the niche preemption model fits best in the three dune habitats. At the 80 m × 80 m and 100 m × 100 m scales, the Volkov neutral model fits best in the fixed and semifixed dune habitats, and the niche preemption model fits best in the mobile dune habitats. In fixed, semifixed, and mobile dunes, both niche and neutral processes played important roles in community construction, reflecting the manifestation of the community niche-neutral continuum.

PERMANOVA testing and Poisson Log-Normal modelling unravel how two traditional cheeses are distinguished through sorting and verbalization tasks

This study uses two statistical methods (PLN modelling and PERMANOVA) to investigate the differences in the ways in which different panels perceive and describe two French uncooked PDO cheeses in a free sorting task and then in a verbalization task.Panelists studied 10 cheeses from two categories Salers and Cantal cheese made from Salers-breed cow’s milk or cow’s milk from other breeds. We selected three types of panel based on their technical expertise in relation to the supply chain (professional technical experts, wholesalers, and consumers) and verified their level of expertise using a knowledge questionnaire to test o their knowledge of cheese in general and Salers and Cantal cheeses in particular. Data from the sorting task was analyzed using the DISTATIS method, and data from the verbalization task was analyzed using a basic correspondence analysis. Furthermore, we employed an original approach mobilising PERMANOVA and a Poisson log-normal (PLN) model enabling us to investigate and quantify which exogeneous variables contribute most to explain verbalization data.The results unsurprisingly showed broadly overlapping cheese configurations between the three panels. However, none of the panels clearly separated Cantal from Salers cheeses. In the verbalization task, different types of panel used different sets of terms to describe the categories. The professional panel preferentially used descriptive terms related to flavor whereas the wholesaler and consumer panels both tended to use quantitative (intensity) and hedonic terms. PLN modelling revealed that the knowledge variable was one of the variables that best explains the use of different word categories between panels. PERMANOVA testing and PLN modelling emerged as novel approaches for identifying the key variables that explain the use of terms in the description task.

Statistical Inference in the Cumulative Exposure Lognormal Model with Hybrid Censoring

This research aims to analyze data coming from step stress life testing experiments where the stress level is incremented at a preset time to obtain failure data faster. To analyze step stress data, a model that extrapolates the information attained from the accelerated tests to normal conditions needs to be fit to the life test data. We used the Cumulative Exposure Model (CEM) to model simple step stress lognormal life test data where hybrid censoring is present and applied the maximum likelihood estimation method to find the point and interval estimates of the parameters. Bootstrap intervals (bootstrap-t intervals and percentile intervals) were also constructed. We then performed a simulation study to assess the proposed methods of estimation under different hybrid censoring schemes. The Bias and MSE of the maximum likelihood estimators (MLEs) along with the coverage probability and average lengths of the corresponding confidence intervals were investigated. Finally, an illustrative example has been used to demonstrate the application of the methods discussed in this paper.

SynSig2Vec: Forgery-Free Learning of Dynamic Signature Representations by Sigma Lognormal-Based Synthesis and 1D CNN.

Handwritten signature verification is a challenging task because signatures of a writer may be skillfully imitated by a forger. As skilled forgeries are generally difficult to acquire for training, in this paper, we propose a deep learning-based dynamic signature verification framework, SynSig2Vec, to address the skilled forgery attack without training with any skilled forgeries. Specifically, SynSig2Vec consists of a novel learning-by-synthesis method for training and a 1D convolutional neural network model, called Sig2Vec, for signature representation extraction. The learning-by-synthesis method first applies the Sigma Lognormal model to synthesize signatures with different distortion levels for genuine template signatures, and then learns to rank these synthesized samples in a learnable representation space based on average precision optimization. The representation space is achieved by the proposed Sig2Vec model, which is designed to extract fixed-length representations from dynamic signatures of arbitrary lengths. Through this training method, the Sig2Vec model can extract extremely effective signature representations for verification. Our SynSig2Vec framework requires only genuine signatures for training, yet achieves state-of-the-art performance on the largest dynamic signature database to date, DeepSignDB, in both skilled forgery and random forgery scenarios. Source codes of SynSig2Vec will be available at https://github.com/LaiSongxuan/SynSig2Vec.

Modelling the kinetics of stearic acid destruction on TiO2 ‘self-cleaning’ photocatalytic films

The kinetics of stearic acid, SA, removal by photocatalytic films are modelled using a log-normal distribution in surface reactivity, which shows that as the distribution in reactivity, ρ, increases, so too does the apparent order of reaction, m, of the observed variation in SA concentration, [SA], versus irradiation time, t. The model is used to fit the observed [SA] vs. t profiles exhibited by three very different TiO2 films, namely Activ™ self-cleaning glass, and prepared sol-gel TiO2 and P25 TiO2 films. These films show decay kinetics, with m = 0.3, 0.44 and 0.6, respectively, which fit the model predicted decay profiles with distribution width, ρ, values, 0.4, 0.54 and 0.7, respectively. A Ag photocatalyst indicator ink is used on these films to highlight the non-uniform distribution in surface reactivity on the micron scale. The use of the log-normal model to better understand the kinetics exhibited by photocatalytic films is discussed briefly.

The distribution of trace contaminants in the manned space station atmosphere

The research is based on the results of air quality monitoring for the period from 2000 to 2020. The air samples have been taken onboard the International Space Station (ISS) using AK-1M samplers and delivered to Earth. The representativeness of the research results is confirmed by the long-term duration (20 years of observation) and the amount of experimental data (analysis of more than 30,000 measured concentrations of chemicals identified by gas chromatography and mass spectrometry). Statistical analysis of measured concentrations showed that the vast majority (70%) of trace contaminants detected in the ISS air have a log-normal distribution, which is confirmed by the use of the Kolmogorov-Smirnov goodness-of-fit test (p > 0.2). For the remaining 30%, the significance level of the Kolmogorov-Smirnov goodness-of-fit criterion was less than 0.2, however, the statistical distributions of these trace contaminants are characterized by unimodality, peakedness (kurtosis coefficient significantly >2) and asymmetry (skewness coefficient >1) with a shift towards lower values, which regarded as a “close to normal distribution”. It has been established that the log-normal model can be accepted as a theoretical model describing the distribution of trace contaminants in the air of manned space stations. The established log-normal distribution and the ratio between the average concentrations of different averaging periods (10 : 3: 1.5 : 1) confirms the uneven nature of air pollutants in the modules and the possibility of the formation of “stagnant” zones. This is of great practical importance, which must be taken into account when establishing the air quality standards for trace contaminants and designing life support systems (ventilation and air purification) for manned space stations.

Analysis on infestation and related ecology of chigger mites on large Chinese voles (Eothenomys miletus) in five provincial regions of Southwest China.

Based on a long-term field investigation in the five provincial regions of Southwest China between 2001 and 2019, the present paper studied the infestation and related ecology of chigger mites (chiggers) on the large Chinese vole (Eothenomys miletus), an endemic and dominant rodent species in the regions. A total of 52331 chiggers were collected from 2661 voles, and 52261 mites were identified as 185 species and 13 genera in the family Trombiculidae with very high species diversity. The identified 185 chigger species on E. miletus (a single rodent species) even exceeded those recorded in some countries. The overall infestation prevalence (Pm = 53.96%), mean abundance (MA = 19.64) and mean intensity (MI = 36.39) on E. miletus were much higher than those on some other rodent species in the same regions. Although the species composition showed a moderate similarity (J = 0.63) between male and female hosts (E. miletus), the infestation indices (Pm = 56.25%, MA = 21.67) of chiggers on male hosts were higher than those on the females (Pm = 51.23%, MA = 17.09) (P < 0.05). Two dominant chigger species, Leptotrombidium scutellare (Cr = 19.17%) and L. sinicum (Cr = 11.06%), showed an aggregated distribution pattern among different individuals of their host E. miletus, and a relatively high degree of positive association existed between the two dominant chigger species with PCC = 0.57, DI = 0.60 and OI = 0.62 (x2 = 857.46, P < 0.001). Leptotrombidium densipunctatum, Walchia koi, Helenicula hsui, L. scutellare and W. ewingi showed a high degree of environmental adaptability to their environments with high niche breadths. The theoretical curve of the species abundance distribution of chigger community on E. miletus was successfully fitted with Preston's lognormal distribution model. Based on the theoretical curve fitting, the expected total number of chigger species on E. miletus was roughly estimated to be 223 species, and 38 chigger species were probably missed in the sampling investigation.

Consumption Expenditure on Processed Meat and Its Correlates: An Ethnic Comparison

Background: The objective of the present study is to investigate the influences of sociodemographic and household factors on consumption expenditure on processed meat among households in Malaysia.Methods: Data were extracted from the Malaysian Household Expenditure Survey (HES) 2016. Lognormal hurdle models were utilized to assess the likelihood of consuming processed meat and the amount consumed. The independent variables consisted of household heads’ age, educational level, gender, marital status, employment status, ethnicity, as well as household income, household region and household locality.Results: Bumiputera households with younger heads were more likely to consume processed meat and spent more than households with older heads. Chinese and Indian households in a higher income group had a higher likelihood of consuming and spending on processed meat than those in a lower income group. The probability of consuming processed meat and the amount consumed were positively associated with being from East Malaysia and urban areas.Conclusions: There are distinguished roles of sociodemographic and household factors across ethnic groups in consumption expenditure on processed meat. Policy makers should take account of age, income, education, household region and household locality factors when formulating intervention measures.

A GMM approach to estimate the roughness of stochastic volatility

We develop a GMM approach for estimation of log-normal stochastic volatility models driven by a fractional Brownian motion with unrestricted Hurst exponent. We show that a parameter estimator based on the integrated variance is consistent and, under stronger conditions, asymptotically normally distributed. We inspect the behavior of our procedure when integrated variance is replaced with a noisy measure of volatility calculated from discrete high-frequency data. The realized estimator contains sampling error, which skews the fractal coefficient toward “illusive roughness.” We construct an analytical approach to control the impact of measurement error without introducing nuisance parameters. In a simulation study, we demonstrate convincing small sample properties of our approach based both on integrated and realized variance over the entire memory spectrum. We show the bias correction attenuates any systematic deviance in the parameter estimates. Our procedure is applied to empirical high-frequency data from numerous leading equity indexes. With our robust approach the Hurst index is estimated around 0.05, confirming roughness in stochastic volatility.

Map-based cosmology inference with lognormal cosmic shear maps

ABSTRACT Most cosmic shear analyses to date have relied on summary statistics (e.g. ξ+ and ξ−). These types of analyses are necessarily suboptimal, as the use of summary statistics is lossy. In this paper, we forward-model the convergence field of the Universe as a lognormal random field conditioned on the observed shear data. This new map-based inference framework enables us to recover the joint posterior of the cosmological parameters and the convergence field of the Universe. Our analysis properly accounts for the covariance in the mass maps across tomographic bins, which significantly improves the fidelity of the maps relative to single-bin reconstructions. We verify that applying our inference pipeline to Gaussian random fields recovers posteriors that are in excellent agreement with their analytical counterparts. At the resolution of our maps – and to the extent that the convergence field can be described by the lognormal model – our map posteriors allow us to reconstruct all summary statistics (including non-Gaussian statistics). We forecast that a map-based inference analysis of LSST-Y10 data can improve cosmological constraints in the σ8–Ωm plane by $\approx\!{30}{{\ \rm per\ cent}}$ relative to the currently standard cosmic shear analysis. This improvement happens almost entirely along the $S_8=\sigma _8\Omega _{\rm m}^{1/2}$ directions, meaning map-based inference fails to significantly improve constraints on S8.

Size distribution of the quasi-circular vegetation patches in the Yellow River Delta, China

Recent empirical studies have suggested that the patch-size distribution of vegetation can be fitted by a power law, truncated power law, or lognormal model to provide explanatory mechanisms for vegetation pattern formation in arid and semiarid regions. However, contradictory results have been reported. Therefore, additional empirical studies are necessary to test the patch-size distribution of vegetation over several regions before it can be considered as an indicator for assessing the discontinuous transition of ecosystems and understanding the mechanisms of vegetation pattern formation. Analogous to arid and semiarid regions of the world, vegetation patterns are characterized by a two-phase mosaic composed of dense vegetation patches interspersed with areas of bare soil, referred to as quasi-circular vegetation patches (QVPs), in the Yellow River Delta (YRD), China. However, research on the patch-size distribution of the QVPs reflecting vegetation patterns and ecosystem functioning is lacking. To fill this gap, for the first time, we examined the patch-size distribution of the QVPs using the fused IKONOS high-spatial-resolution image and evaluated the statistical distributions that better fit the patch size data of the QVPs in the YRD. We found that a power law, truncated power law, or lognormal distribution was not supported in the study area, whereas gamma distribution reasonably fits the size data of QVPs, implying that micro-depressions, combined with the water-limited and salinization environments had considerable effects on vegetation pattern formation. Our results provide helpful insights and suggest that further studies are needed to classify different types of QVPs. Additionally, more efficient approaches need to be used to fit the statistical distributions for elucidating the spatial vegetation patterns in the YRD.

Improved estimators for analyzing highly skewed environmental datasets with detection limits

The datasets from environmental studies often contain some measurements that fall below some detection limits. These datasets are often highly skewed making most of the standard models inappropriate to model these data. In order to investigate such data, the mixture models under classical methods have been proposed in the literature. In the case of mixture models, the mixture of gamma and lognormal models has frequently been used. We have proposed the mixture model under the Bayesian approach to analyze the said datasets. Two real skewed datasets with detection limits have been used for the analysis. On comparing with a variety of mixture models, the two-component mixture of Frechet distributions (2CMFD) has been explored to be the most suitable model for modelling highly skewed datasets. In addition, the performance of the proposed Bayes estimators was better than that of those existing in the literature.

Anchoring Options on Variance and Volatility to Terminal Risk Neutral Distribution

In this paper the ratio of realized variance to the terminal squared return is modeled as independently distributed. Variance and volatility options are then first priced conditional on the terminal stock price. The variance and volatility options and their risk exposures are associated with option portfolios hedging the conditional price function. In particular the volatility swap vega is observed to be near a point above the variance swap vega. The residual uncertainty given the terminal stock price is modeled both using a log normal model and the empirical distribution.

Parametric frailty models under two-parameter Lindley distribution with applications to time-to-event analysis

A frailty model is a random effects model in survival or time-to-event analysis, where the random effect (the frailty) has a multiplicative effect on the hazard. Lindley distribution is one of the classical distributions, which is widely used in reliability and ordinary survival models (without frailty) but not in the frailty models. In recent years, Lindley distribution and its generalizations have played an important role in survival analysis due to its natural flexibility. In this study, we attempt to fit parametric frailty models with Two-parameter Lindley baseline distribution (TPLD) and apply them to the two real-life disease data sets of the (i) Recurrent asthma attacks in children’s (Asthma attacks) and (ii) Culling of dairy heifer cow’s (Culling) data. Comparison and assed the model's fitness were done using a minimum value of Akaike's Information Criteria (AIC) and Bayesian Information Criteria (BIC). The study results revealed that TPLD with the Lognormal frailty model is a good choice for Culling data and Lindley with Gamma frailty model is the best for Asthma data. So, we suggest that the Two-parameter Lindley baseline distribution (TPLD) with frailty models are potential alternative models and will facilitate analyses of time-to-event data with covariates.

Differences in Discrimination with Respect to Latent Trait and Test-Taking Speed Across Items Measuring Sub-Domains of Cognitive Ability

The relationship between latent trait and test-taking speed is an important area of study in assessment research. In addition to contributions of such studies to psychometrics, the factors that affect both ability and speed have implications for test development and have policy consequences especially if the tests are high stakes. This study investigated the main assessment scale used in gifted education screening in the Kingdom of Saudi Arabia and focused on the discriminating properties of items across the several cognitive subskills being measured. Under an item response theoretic framework, this study used a lognormal response time model to investigate the discrimination parameter estimates for both ability and speed, with guessing taken into account. Results showed that cognitive subskills do not have uniform discrimination properties across ability and speed, such that some types of items are better at discriminating ability while other types are better at discriminating speed. At a test-level, our results also showed that ability is negatively correlated with speed, such that higher ability students tend to take more time and hence have slower speed. This finding supports other results in the literature. Implications for high-stakes testing and test development are discussed.

Development of ecological risk assessment for Diisobutyl phthalate and di-n-octyl phthalate in surface water of China based on species sensitivity distribution model

Phthalic acid esters (PAEs) are commonly used as plasticizer and are emerging concern worldwide for potent adverse effects of aquatic organisms. Certain PAEs were often detected in different environmental matrices but related toxicity data were still lacking to support their risk assessment. The study investigated the acute toxicity of Diisobutyl phthalate (DiBP) and Di-n-octyl phthalate (DnOP) using 6 Chinese resident aquatic organisms from 3 phyla and 6 species and constructed the species sensitivity distribution (SSD) models for ecological risk assessment. Lethal concentration 50% (LC50) ranges of DiBP and DnOP were 4.89–21.45 mg/L and 1.45–1200 mg/L, respectively. The derived acute and chronic predicted no-effect concentrations (PNECs) based on log-normal model of water were 0.54 and 0.04 mg/L for DiBP and 0.23 and 0.05 mg/L for DnOP, respectively. The ERA for DiBP and DnOP in the surface water and sediment of China was conducted. Water samples of Haihe Rive (RQ = 0.41) and Hun River (RQ = 0.16) of DiBP showed medium risk. And sediment samples of Yellow River (RQ = 0.71) and Chao Hu Lake (RQ = 0.42) of DiBP showed medium risk. Meanwhile, the above water and sediment samples (RQ＜0.1) of DnOP showed low risk.