Lognormal Mixture Research Articles

Use of emergency departments by children and young people following telephone triage: a large database study

BackgroundAlthough one objective of NHS 111 is to ease the strain on urgent and emergency care services, studies suggest the telephone triage service may be contributing to increased demand. Moreover,...

Loss modeling with the size-biased lognormal mixture and the entropy regularized EM algorithm

The Erlang mixture with a common scale parameter is one of many popular models for modeling insurance losses. However, the actuarial literature recognizes and discusses some limitations of aforementioned model in approximate heavy-tailed distributions. In this paper, a size-biased left-truncated Lognormal (SB-ltLN) mixture is proposed as a robust alternative to the Erlang mixture for modeling left-truncated insurance losses with a heavy tail. The weak denseness property of the weighted Lognormal mixture is studied along with the tail behavior. Explicit analytical solutions are derived for moments and Tail Value at Risk based on the proposed model. An extension of the regularized expectation–maximization (REM) algorithm with Shannon's entropy weights (ewREM) is introduced for parameter estimation and variability assessment. The Operational Riskdata eXchange's left-truncated internal fraud loss data set is used to illustrate applications of the proposed model. Finally, the results of a simulation study show promising performance of the proposed SB-ltLN mixture in different simulation settings.

Multivariate lognormal mixture for pulp particle characterization

AbstractWe present a method for pulp particle characterization based on a truncated lognormal mixture (TLM) model, as motivated by size statistics of organisms. We use an optical fiber analyzer to measure the length–width distribution of kraft-cooked roundwood or sawmill sources, of chemi-thermomechanical pulp (CTMP) samples from roundwood or sawmill sources, and the same CTMP samples after kraft post-processing. Our results show that bimodal TLMs capture salient features of the investigated pulp particle distributions, by decomposition into a large-particle and a small-particle fraction. However, we find that fibers from sawmill sources, which have not undergone mechanical treatment, cannot be described by TLM, likely due to non-random sampling. Within the confines of our dataset, the TLM characterization predicts laboratory sheet properties more effectively than conventional averaging methods for pulp particle size distributions. The TLM characterization is intended as a tool for controlling the pulp production process towards higher product quality, uniformity, and energy efficiency, pending further mill trials for validation.

Providing evidence for the conservation of a rare forest butterfly: Results from a three-year capture-mark-recapture study

Species living in spatially structured populations require a network of interconnected habitat patches. Due to changes in forest management, this network of habitat patches has been lost for insect species inhabiting open spots within forests. We studied two of the last populations of the Southern White Admiral (Limenitis reducta) in Germany. The aim of our study was to provide information for the conservation of this species. We conducted a capture-mark-recapture study over three consecutive years and we estimated population sizes and demographic parameters using Jolly-Seber and Cormack-Jolly-Seber models. Furthermore, we used different dispersal kernels to study the dispersal of L. reducta. We found that apparent survival rates differed greatly between the sexes. The mean residence times were eight to nine days for males and only two to four days for females. Apparent survival rates of both sexes decreased with increasing wing deterioration. Total population sizes of L. reducta varied between sites and years and ranged between 61 and 123. Daily abundances were generally low, especially that of females. The mean dispersal distance of individual recaptured butterflies increased in years with higher population densities, suggesting density-dependent dispersal. The dispersal data in our study was clearly bimodal, probably reflecting ‘routine movement’ at short distances and ‘displacement movement’ between habitat patches at longer distances. Consequently, the processes generating the dispersal data were better represented by the lognormal mixture model than by the negative exponential and the inverse power function. The mixed kernel predicted that about 9 % of the population disperses over > 1 km but that long-distance dispersal is rare. Our study highlights the urgent need for conservation measures to protect L. reducta in Germany and, based on our data, we recommend to create new habitat patches at distances of 1 to 1.5 km from existing habitats.

Multivariate count time series segmentation with “sums and shares” and Poisson lognormal mixture models: a comparative study using pedestrian flows within a multimodal transport hub

Multivariate count time series segmentation with “sums and shares” and Poisson lognormal mixture models: a comparative study using pedestrian flows within a multimodal transport hub

BRAQUE: Bayesian Reduction for Amplified Quantization in UMAP Embedding.

Single-cell biology has revolutionized the way we understand biological processes. In this paper, we provide a more tailored approach to clustering and analyzing spatial single-cell data coming from immunofluorescence imaging techniques. We propose Bayesian Reduction for Amplified Quantization in UMAP Embedding (BRAQUE) as an integrative novel approach, from data preprocessing to phenotype classification. BRAQUE starts with an innovative preprocessing, named Lognormal Shrinkage, which is able to enhance input fragmentation by fitting a lognormal mixture model and shrink each component towards its median, in order to help further the clustering step in finding more separated and clear clusters. Then, BRAQUE's pipeline consists of a dimensionality reduction step performed using UMAP, and a clustering performed using HDBSCAN on UMAP embedding. In the end, clusters are assigned to a cell type by experts, using effects size measures to rank markers and identify characterizing markers (Tier 1), and possibly characterize markers (Tier 2). The number of total cell types in one lymph node detectable with these technologies is unknown and difficult to predict or estimate. Therefore, with BRAQUE, we achieved a higher granularity than other similar algorithms such as PhenoGraph, following the idea that merging similar clusters is easier than splitting unclear ones into clear subclusters.

Volatility surfaces and log-normal mixture: Crafting the perfect arbitrage-free calibration

Volatility surfaces and log-normal mixture: Crafting the perfect arbitrage-free calibration

Poverty and Inequality Mapping Based on a Unit-Level Log-Normal Mixture Model

AbstractEstimating poverty and inequality parameters for small sub-populations with adequate precision is often beyond the reach of ordinary survey-weighted methods because of small sample sizes. In small area estimation, survey data and auxiliary information are combined, in most cases using a model. In this paper, motivated by the analysis of EU-SILC data for Italy, we target the estimation of a selection of poverty and inequality indicators, that is mean, headcount ratio and quintile share ratio, adopting a Bayesian approach. We consider unit-level models specified on the log transformation of a skewed variable (equivalized income). We show how a finite mixture of log-normals provides a substantial improvement in the quality of fit with respect to a single log-normal model. Unfortunately, working with these distributions leads, for some estimands, to the non-existence of posterior moments whenever priors for the variance components are not carefully chosen, as our theoretical results show. To allow the use of moments in posterior summaries, we recommend generalized inverse Gaussian distributions as priors for variance components, guiding the choice of hyperparameters.

TppFaaS: Modeling Serverless Functions Invocations via Temporal Point Processes

Serverless computing is a cloud computing paradigm that allows developers to focus exclusively on business logic as cloud service providers manage resource management tasks. Serverless applications based on this model are often composed of several fine-grained and ephemeral Function-as-a-Service (FaaS) functions that implement complex business processes via mutual interaction and interaction with Backend-as-a-Services (BaaS) such as databases. FaaS functions suffer from the cold start problem because of the scale to zero instances feature. In this work, we use neural Temporal Point Processes (TPPs) to model function invocations in FaaS compositions. A probability distribution over the time and class of the following invocations for a given history of invocations is predicted using these probabilistic models. The prediction can avoid cold starts by scaling functions in advance and reduce network load by optimizing the function-server assignment. In this regard, we developed a python-based tool called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">TppFaaS</i> on top of OpenWhisk open-source serverless platform. TppFaaS uses the neural TPPs LogNormMix for modeling the time using a log-normal mixture distribution and TruncNorm for predicting a single value for the time. Furthermore, we built a custom trace data collector for OpenWhisk embedded into TppFaaS and created datasets for multiple FaaS compositions to train and test our models. For datasets without cold starts, the models achieved for most compositions a mean absolute error below 22ms and a percentage of correctly predicted function classes above 94%.

Lognormal and log-logistic distribution mixture analysis and application

In this paper, we analyze a mixture of Lognormal and Log-Logistic distribution. We estimate the parameters of the introduced distribution by using the expectation-maximization (EM) algorithm. Various phenomena in the field of medicine and economy could be modeled by this mixture. In this paper, it is used to construct new mortality model for determining the unisex premium rates in life insurance. The application of the model is illustrated in the case of Serbian population and its advantages are presented in the context of life insurance premium calculation.

PROBABILISTIC ANALYSIS OF THE MAXIMAL LOAD OF INDUSTRIAL MACHINES

This study describes the statistical analysis of peak forces of industrial washing machines. The data source comes from twelve different machines. The measurements are done using a force gauge installed in places for fastening screws. A new software based on LabView has been developed to gauge the acting forces. To determine extreme force values, various probability distributions are applied. Furthermore, a convex combination of lognormal distribution is used in more complicated cases. The parameters of the lognormal mixtures are determined using modified an Expectation-maximization algorithm. Finally, the achieved results are interpreted with regard to the engineering design and to the operating reliability.

A probabilistic model for the ultradian timing of REM sleep in mice.

A salient feature of mammalian sleep is the alternation between rapid eye movement (REM) and non-REM (NREM) sleep. However, how these two sleep stages influence each other and thereby regulate the timing of REM sleep episodes is still largely unresolved. Here, we developed a statistical model that specifies the relationship between REM and subsequent NREM sleep to quantify how REM sleep affects the following NREM sleep duration and its electrophysiological features in mice. We show that a lognormal mixture model well describes how the preceding REM sleep duration influences the amount of NREM sleep till the next REM sleep episode. The model supports the existence of two different types of sleep cycles: Short cycles form closely interspaced sequences of REM sleep episodes, whereas during long cycles, REM sleep is first followed by an interval of NREM sleep during which transitions to REM sleep are extremely unlikely. This refractory period is characterized by low power in the theta and sigma range of the electroencephalogram (EEG), low spindle rate and frequent microarousals, and its duration proportionally increases with the preceding REM sleep duration. Using our model, we estimated the propensity for REM sleep at the transition from NREM to REM sleep and found that entering REM sleep with higher propensity resulted in longer REM sleep episodes with reduced EEG power. Compared with the light phase, the buildup of REM sleep propensity was slower during the dark phase. Our data-driven modeling approach uncovered basic principles underlying the timing and duration of REM sleep episodes in mice and provides a flexible framework to describe the ultradian regulation of REM sleep in health and disease.

A LMM-based seismic fragility analysis method for bridges

The common seismic fragility analysis methods are mainly inaccurate due to assumptions made in derivation process or time consuming because of large sample analysis. A new approach based on lognormal mixture model (LMM) is presented for seismic fragility analysis of long-span bridges, where LMM is used to calculate the structural demand distributions and the seismic fragility is obtained through cumulative distribution function. To demonstrate the feasibility of the present approach, seismic fragility analysis is carried out on a long-span suspension bridge with a main span of 1200m. The results show that the present approach has higher accuracy than the classical approach.

Modeling road traffic accidents in Mauritius using clustered longitudinal COM-Poisson with gamma random effects

This article proposes a nonstationary clustered longitudinal model to analyze road traffic accident time series data from 2016 to 2017 in Mauritius. The Conway–Maxwell–Poisson model (COM-Poisson) is used as the baseline model with gamma-distributed random effects (CMP-G). Several time-variant explanatory variables are incorporated into the model specification link predictor to identify the likely causes of road crashes in the Mauritius. The proposed model competes with the popular Poisson gamma and log-normal mixtures when modeling over-dispersion. The model parameters namely the regression, serial, and dispersion effects, are estimated suitably by a generalized quasi-likelihood (GQL) estimation method while the serial parameter is treated as nuisance and estimated by method of moments. The asymptotic properties of the GQL estimators are discussed. A simulation study based on an integer-valued auto-regressive of order 1 structure (INAR(1)) with CMP-G distributed innovation terms, is also proposed to assess the performance of GQL based on the CMP-G. Data application is of road traffic accidents in Mauritius where some model criteria have been computed to assess the goodness of fits of the proposed model against the Poisson-gamma and Poisson-log normal mixtures.

Origin-Destination-Based Travel Time Reliability under Different Rainfall Intensities: An Investigation Using Open-Source Data

Origin-destination- (O-D-) based travel time reliability (TTR) is fundamental to next-generation navigation tools aiming to provide both travel time and reliability information. While previous works are mostly focused on route-based TTR and use either ad hoc data or simulation in the analyses, this study uses open-source Uber Movement and Weather Underground data to systematically analyze the impact of rainfall intensity on O-D-based travel time reliability. The authors classified three years of travel time data in downtown Boston into one hundred origin-destination pairs and integrated them with the weather data (rain). A lognormal mixture model was applied to fit travel time distributions and calculate the buffer index. The median, trimmed mean, interquartile range, and one-way analysis of variance were used for quantification of the characteristics. The study found some results that tended to agree with the previous findings in the literature, such that, in general, rain reduces the O-D-based travel time reliability, and some seemed to be unique and worthy of discussion: firstly, although in general the reduction in travel time reliability gets larger as the intensity of rainfall increases, it appears that the change is more significant when rainfall intensity changes from light to moderate but becomes fairly marginal when it changes from normal to light or from moderate to extremely intensive; secondly, regardless of normal or rainy weather, the O-D-based travel time reliability and its consistency in different O-D pairs with similar average travel time always tend to improve along with the increase of average travel time. In addition to the technical findings, this study also contributes to the state of the art by promoting the application of real-world and publicly available data in TTR analyses.

An Iterative Approach to Stratification: Poverty at Regional Level in Italy

We develop an iterative procedure to generate stratification in non-overlapping classes of a population based on a one-dimensional variable, namely, the Italian income. The procedure works under the assumption that the income distribution is generated by a log-normal mixture of homogeneous income groups. The number of income groups is not determined a priori but rather endogenously by the iterative procedure that stops when the solution to a specific second-degree polynomial equation does not exist. We apply the approach to study the heterogeneity of Italian incomes and the poor population at regional level in the years 2005, 2010, and 2015. The cross-regional comparisons show differences in inequality and stratification dynamics while comparisons over time show the evolution of the classes.

Characterization of Daily Travel Distance of a University Car Fleet for the Purpose of Replacing Conventional Vehicles with Electric Vehicles

This study attempts to fit daily travel distances (DTD) data collected from the Nagoya University (NU) car-sharing system for one year to several distribution functions, including a lognormal mixture model. It is deemed here that the lognormal distribution performs best among the five tested single-distribution functions based on their p-values. Moreover, the lognormal mixture model can represent the driving pattern better overall with respect to the Akaike information criterion (AIC). Taking two types of electric vehicles (EVs) into consideration, the results show that 30 out of 48 vehicles can be substituted by the EV type with a larger battery capacity according to the observed DTD data and when a 95% confidence level is considered. In this exercise, the updated car-sharing system can have up to nine available vehicles at peak hour, which can reach the peak-shaving need and provides the possibility of contributing electricity for common use with the help of the vehicle-to-grid (V2G) system. Additionally, the updated system with a larger battery capacity can also reduce 24% of the CO2 emissions. These types of systems could be widely applied to other organizations or companies in the consideration of electricity consumption and emission reduction.

The Optimal Morphological Model for Arterial Blood Pressure Wave Related Classification: Comparison of Two Types of Kernel Function Mixtures

The morphological modeling methods are efficient in quantifying the change of arterial blood pressure (ABP) waves. The related works focus on minimizing the modeling error but ignore the classification related modeling expression in practical applications. In this study, we explored the optimal modeling method for ABP wave related classifications. Two types of conventional models, Gaussian or Lognormal kernel function mixtures, were employed to quantitively describe the change of ABP signals, and the parameters of different models were engaged to train the different classifiers by probabilistic neural network (PNN) and random forest (RF) for identifying the ABP waves by age, gender, and whether belonging to extreme bradycardia (EB) or extreme tachycardia (ET). Then, we defined some indexes about the performance of modeling and classifications as the references to compare the different models. The ABP signals of Fantasia and 2015 PhysioNet/CinC Challenge databases were exploited as the experimental data to select the optimal model. The modeling results show that the Lognormal kernel function mixtures have a lower error in ABP wave modeling. The two-sample Kolmogorov-Smirnov test (ks-test) results indicate that the parameters of all models are markedly different at a highly significant level (h = 1, p <; 0.05) between different groups. The classification results show that the classifiers based on the four-Gaussian function model have the best performance with the average Kappa coefficients (KC) of 99.160 ± 0.123%, while the average KC for the classifiers of two-Lognormal function models is 97.585 ± 0.172%, which means there is excessive information redundancy in the classifications by the three and four kernel functions models. Considering some other indexes such as time consumption and RAM space, the 2 Lognormal function model has more potential in practical applications.

Advanced spatial modulation for efficient MIMO‐based B2B communications in sporting activities

In this study, advanced multiple-input multiple-output (MIMO) techniques for body-to-body (B2B) sensor-based communication for sporting activities like running and cycling under different scenarios have been proposed. Enhanced spatial modulation and spatial media-based modulation have been investigated for efficient MIMO-based B2B communication. Special sensors have been proposed to deploy such techniques. Lognormal (LN) mixture model has been used because it can address the shadowing effects in B2B communication for such activities. Since LN mixture cannot yield closed-form expressions, it has been approximated using mixture of gamma (MG) distribution to achieve closed-form expressions for bit error rate (BER) in MIMO-based B2B communication for the first time. The system performance for the proposed methods has been analysed in terms of BER and theoretical upper bound expressions using MG distribution have been verified by Monte Carlo simulations.

Numerical analysis and experimental validation of hydrodynamics of a thin bubbling fluidized bed for various particle-size distributions using a three-dimensional dense discrete phase model

A dense discrete phase model combined with the kinetic theory of granular flows was used to study the bubbling characteristics and segregation of poly-dispersed particle mixtures in a thin fluidized bed. Our simulations showed that in using the hybrid Eulerian–Lagrangian method, the common use of one computational cell in the thickness direction of the thin bed does not predict wall friction correctly. Instead, a three-cell discretization of the thickness direction does predict the wall friction well but six cells were needed to prevent overprediction of the bed expansion. The change in specularity factor (SF) of the model not only affected the predictions of the velocity of particles, but also had a considerable impact on their flow pattern. A decrease in SF, which decreases wall friction, showed an over-prediction in the size of bubbles, particle velocities, and void fraction of the bed, and led to a shift in the circulation center toward the bottom of the bed. The segregation of the Geldart B particles was studied in the narrow range from 400 to 600μm with a standard deviation less than 10% of the average diameter. Simulations showed that large particles accumulated close to the distributor at the bottom of the bed and the center of the bed, but small particles moved towards the wall and top surface. The decrease in the mean particle size and spread in shape of the distribution improves mixing by up to 30% at a superficial gas velocity of around 2.5 times the minimum fluidization velocity. Log-normal mixtures with a small proportion of large particles had the most uniform distribution with a thin layer of jetsam forming at the bottom of the bed. Finally, experimental verification of the segregation and mixing of polydisperse particles with narrow size distribution is suggested.