Distribution Fitting Research Articles

A Novel Goodness-of-Fit Test for Lifetime Models Based on Type II Censored Data

In this paper, a novel test statistic is introduced to evaluate the goodness of fit of lifetime distributions when dealing with Type II censored data. The test statistic is derived from a local linear regression-based estimator of the Kullback–Leibler information. Extensive analysis is conducted to examine the properties of this test statistic, highlighting its nonnegative nature, as for KL information. The proposed test statistic is applied to various distributions, namely exponential, Weibull, log-normal, and Pareto. Critical values and Type I error rates for the tests are determined, demonstrating their exceptional accuracy and reliability. To further assess their performance, the proposed tests are subjected to Monte Carlo simulations, comparing their power values against alternative tests currently in use. Finally, the proposed method is applied to three real data sets from the engineering reliability aspect to prove their practical versatility.

Best fitting probability distributions of monthly rainfall extremes in Nasiriyah city, southern Iraq

Best fitting probability distributions of monthly rainfall extremes in Nasiriyah city, southern Iraq

Rigorous Analysis of Multimodal HDX-MS Spectra.

An inherent strength of hydrogen/deuterium exchange coupled to mass spectrometry (HDX-MS) is its ability to detect the presence of multiple conformational states of a protein, which often manifest as multimodal isotopic envelopes. However, the statistical considerations for accurate analysis of multimodal spectra have yet to be established. Here we outline an unrestrained binomial distribution fitting approach with the corresponding statistical tests to accurately detect and, when possible, deconvolute isotopic distributions that contain multiple subpopulations. The algorithms have been incorporated into an updated version of the freely available software, HX-Express, and validated using known mixtures of peptides deuterated to varying degrees. This approach presents a readily accessible tool to fit and interpret bimodal and trimodal behavior in HDX-MS data for mixed populations, EX1 kinetics, and pulse labeling data.

Analysis and Flood Mapping of Pekalen Watershed of Probolinggo Regency Using HEC-RAS Application

Flooding is one of the natural disasters that needs attention, especially in the Pekalen watershed, Probolinggo Regency. The purpose of this research is to analyze the design flood discharge and mapping of the area potentially affected by inundation. The research stages began with arithmetic area average rainfall analysis, log pearson type III design rainfall analysis, chi squared and smirnov-kolmogorov distribution fit test, mononobe rainfall intensity, HSS Nakayasu design flood discharge analysis, and flood mapping with HEC-RAS 2D flood modeling. The design flood discharge of Pekalen watershed at 10-year return period is 421.4 m³/s, 25-year return period is 455.12 m³/s, and 50-year return period is 479 m³/s. The areas potentially affected by inundation at 25 years return periods are Sukomulyo, Sukokerto, Pajarakankulon, Kradenan, Tanjung, Karangbong, Temenggungan, Karanggeger, Ketompen, Petemon, Selogudigwetan, Selogudigkulon, Puspan, Braniwetan, Branilor, Sumbersecang, Satreyan, Maronkidul, Gerongan, Brabe, Condong, Racek, Pesawaran, Ranugedang, Jangkang, Segaran, Ranuagung, Tiris, Andungsari, Andungbiru, and Sumberaren.

A novel method for evaluating asphalt pavement structural performance based on vehicle vibration

ABSTRACT Fast, accurate, and high-frequency detection for evaluating pavement structural performance is vital for road maintenance decision-making. Traditional detection methods make it challenging to balance the detection speed, frequency, and cost. Pavement condition identification technology based on vehicle vibration has become increasingly mature and can overcome the above problems. This study aims to evaluate the structural performance of asphalt pavement. A vehicle-based test system based on two-axle vibration sensing was developed. The vibration signal from the vehicle driving in the asphalt pavement was generated. Further, the deep signal features was extracted based on the expression of the probability distribution. The evolutionary characteristics of probability density distribution and cumulative distribution were summarized. The main conclusions are as follows: The theoretical model analyzed the correlation between the probability density and the pavement modulus. Further, estimate the peak of the probability density (PKDE) and the cumulative distribution fitting value (CDF0). The estimated indexes’ correlation coefficients were calculated by matching the dynamic deflection index of 10 road sections. As a result, PKDE has a robust correlation with a correlation coefficient of 0.81. Therefore, the vehicle vibration probability distribution expression method proposed is effective for structural performance evaluation and has high application feasibility.

The generalized Hausman test for detecting non-normality in the latent variable distribution of the two-parameter IRT model.

This paper introduces the generalized Hausman test as a novel method for detecting the non-normality of the latent variable distribution of the unidimensional latent trait model for binary data. The test utilizes the pairwise maximum likelihood estimator for the parameters of the latent trait model, which assumes normality of the latent variable, and the maximum likelihood estimator obtained under a semi-non-parametric framework, allowing for a more flexible distribution of the latent variable. The performance of the generalized Hausman test is evaluated through a simulation study and compared with other test statistics available in the literature for testing latent variable distribution fit and an overall goodness-of-fit test statistic. Additionally, three information criteria are used to select the best-fitted model. The simulation results show that the generalized Hausman test outperforms the other tests under most conditions. However, the results obtained from the information criteria are somewhat contradictory under certain conditions, suggesting a need for further investigation and interpretation. The proposed test statistics are used in three datasets.

EPOCHS. IV. SED Modeling Assumptions and Their Impact on the Stellar Mass Function at 6.5 ≤ z ≤ 13.5 Using PEARLS and Public JWST Observations

We utilize deep JWST Near Infrared Camera (NIRCam) observations for the first direct constraints on the Galaxy Stellar Mass Function (GSMF) at z > 10. Our EPOCHS v1 sample includes 1120 galaxy candidates at 6.5 < z < 13.5 taken from a consistent reduction and analysis of publicly available deep JWST NIRCam data covering the Prime Extragalactic Areas for Reionization Science, CEERS, GLASS, JADES GOOD-S, NGDEEP, and SMACS0723 surveys, totaling 187 arcmin2. We investigate the impact of spectral energy distribution fitting methods, assumed star formation histories (SFHs), dust laws, and priors on galaxy masses and the resultant GSMF. While our fiducial GSMF agrees with the literature at z < 13.5, we find that the assumed SFH model has a large impact on the GSMF and stellar mass density (SMD), finding a 0.75 dex increase in the SMD at z = 10.5 between a flexible nonparametric and standard parametric SFH. Overall, we find a flatter SMD evolution at z ≥ 9 than some studies predict, suggesting a rapid buildup of stellar mass in the early Universe. We find no incompatibility between our results and those of standard cosmological models, as suggested previously, although the most massive galaxies may require a high star formation efficiency. We find that the “little red dot” galaxies dominate the z = 7 GSMF at high masses, necessitating a better understanding of the relative contributions of active galactic nucleus and stellar emission. We show that assuming a theoretically motivated top-heavy initial mass function (IMF) reduces stellar mass by 0.5 dex without affecting fit quality, but our results remain consistent with existing cosmological models with a standard IMF.

Spectral Energy Distribution Modeling of BL Lacertae during a Large Submillimeter Outburst and Low X-Ray Polarization State

Abstract In 2023 October–November, the blazar BL Lacertae underwent a very large-amplitude submillimeter outburst. The usual single-zone leptonic model with the lower-energy peak of the spectral energy distribution (SED) fit by the synchrotron emission from one distribution of relativistic electrons in the jet and inverse-Compton (IC) scattering of lower-energy photons from the synchrotron radiation in the jet itself (synchrotron self-Compton or SSC) or those from the broad-line region and torus by the same distribution of electrons cannot satisfactorily fit the broadband SED with simultaneous data at submillimeter, optical, X-ray, and GeV energies. Furthermore, simultaneous observations with IXPE indicate the X-ray polarization is undetected. We consider two different synchrotron components, one for the high flux in the submillimeter wavelengths and another for the data at the optical band, which are supposedly due to two separate distributions of electrons. In that case, the optical emission is dominated by the synchrotron radiation from one electron distribution, while the X-rays are mostly due to SSC process by another, which may result in low polarization fraction due to the IC scattering. We show that such a model can fit the broadband SED satisfactorily as well as explain the low polarization fraction at the X-rays.

Consumer Search and Product Line Length: The Role of the Consumer-Product Fit Distribution

We examine the impact of consumer search on firms’ product line strategy and show how it critically depends on consumer-product fit distribution.

A spectrophotometric analysis and dust properties of classical nova V5584 Sgr

ABSTRACT In this work, optical observations of the nova V5584 Sgr are presented. These observations cover different phases including pre-maximum, early decline, and nebular. The spectra are dominated by hydrogen Balmer, Fe ii, and O i lines with P-Cygni profiles in the early phase, which are subsequently observed in complete emission. The presence of numerous Fe ii lines and low ejecta velocity aligns with the Fe ii type nova classification. From optical and NIR colours, it is clear that this nova manifests dust formation in the ejecta. The dust temperature and mass were estimated from a spectral energy distribution (SED) fit to the JHK band magnitudes and the Wide field Infrared Survey Explorer data. Light-curve analysis shows t$_2$ and t$_3$ values of $\sim$ 26 and $\sim$ 48 d, classifying the nova as moderately fast. The physical and chemical properties during early decline and later phases were evaluated using the photoionization code CLOUDY. The best-fitting model parameters from two epochs of multiwavelength spectra are compatible with a hot white dwarf source with a roughly constant luminosity of $\sim$(2.08 $\pm$ 0.10) $\times$ 10$^{36}$ erg s$^{-1}$. We find an ejected mass of $\sim$(1.59 $\pm$ 0.04) $\times$ 10$^{-4}$ M$_{\odot }$. Abundance analysis indicates that the ejecta is significantly enriched relative to solar values, with O/H = 30.2, C/H = 10.8, He/H = 1.8, Mg/H = 1.68, Na/H = 1.55, and N/H = 45.5 in the early decline phase, and O/H = 4.5, Ne/H = 1.5, and N/H = 24.5 in the nebular phase.

The Resolved Behavior of Dust Mass, Polycyclic Aromatic Hydrocarbon Fraction, and Radiation Field in ∼800 Nearby Galaxies

We present resolved 3.6–250 μm dust spectral energy distribution (SED) fitting for ∼800 nearby galaxies. We measure the distribution of radiation field intensities heating the dust, the dust mass surface density (Σd), and the fraction of dust in the form of polycyclic aromatic hydrocarbons (PAHs; q PAH). We find that the average interstellar radiation field ( U¯ ) is correlated both with stellar mass surface density (Σ⋆) and star formation rate surface density (ΣSFR), while more intense radiation fields are only correlated with ΣSFR. We show that q PAH is a steeply decreasing function of ΣSFR, likely reflecting PAH destruction in H ii regions. Galaxy-integrated q PAH is strongly, negatively correlated with specific star formation rate (sSFR) and offset from the star-forming “main sequence” (ΔMS), suggesting that both metallicity and star formation intensity play a role in setting the global q PAH. We also find a nearly constant M d/M * ratio for galaxies on the main sequence, with a lower ratio for more quiescent galaxies, likely due to their lower gas fractions. From these results, we construct prescriptions to estimate the radiation field distribution in both integrated and resolved galaxies. We test these prescriptions by comparing our predicted U¯ to results of SED fitting for stacked “main-sequence” galaxies at 0 < z < 4 from M. Béthermin et al. and find sSFR is an accurate predictor of U¯ even at these high redshifts. Finally, we describe the public delivery of matched-resolution Wide-field Infrared Survey Explorer and Herschel maps along with the resolved dust SED-fitting results through the Infrared Science Archive.

Distribution characteristics of the summer precipitation raindrop spectrum on the Qinghai–Tibet Plateau

Abstract. To enhance the precision of precipitation forecasting in the Qinghai–Tibet Plateau region, a comprehensive study of both macro- and micro-characteristics of local precipitation is imperative. In this study, we investigated the particle size distribution, droplet velocity, droplet number density, Z–I (radar reflectivity–rainfall intensity) relationship, and gamma distribution of precipitation droplet spectra with a single precipitation duration of at least 20 min and precipitation of 5 mm or more at four stations (Nyalam, Lhasa, Shigatse, and Naqu) in Tibet during recent years from June to August. The results are as follows: (1) in the fitting relationship curve between precipitation raindrop spectral particle size and falling speed at the four stations in Tibet, when the particle size was less than 1.5 mm, the four lines essentially coincided. When the particle size exceeded 1.5 mm, the speed in Nyalam was the highest, followed by Naqu, and the speed in Lhasa was the lowest. The falling speed of particles correlated with altitude. (2) The five microphysical characteristics (mean diameter (Dm), average volume diameter (Dv), mode diameter (Dd), dominant diameter (Dp), and median diameter (Dnd)) at the four stations have different correlation relationships with altitude under different rainfall intensities. Dm exhibits a negative correlation with altitude at the same rainfall intensity; in contrast, Dv shows a positive correlation with altitude. For microphysical parameters such as Dd and Dp, a rainfall intensity of 10 mm h−1 serves as the boundary line, and they have different correlation relationships with altitude under the same rainfall intensity level. (3) The Z–I relationships at the four stations exhibited variations. Owing to the proximity in altitude between Lhasa and Shigatse, as well as between Nyalam and Nagqu, the coefficient a and index b in the Z–I relationships of the two groups of sites were relatively similar. (4) The fitting curves of the exponential and gamma distributions of the precipitation particle size at the aforementioned four stations are largely comparable. The exponential distribution fitting exhibits a slightly better effect. The parameter μ in the gamma distribution decreases with an increase in altitude, while N0 and λ in the exponential distribution show a clear upward trend with altitude.

The multiple classes of ultra-diffuse galaxies: Can we tell them apart?

Abstract This study compiles stellar populations and internal properties of ultra-diffuse galaxies (UDGs) to highlight correlations with their local environment, globular cluster (GC) richness, and star formation histories. Complementing our sample of 88 UDGs, we include 36 low-surface brightness dwarf galaxies with UDG-like properties, referred to as NUDGes (nearly-UDGs). All galaxies were studied using the same spectral energy distribution fitting methodology to explore what sets UDGs apart from other galaxies. We show that NUDGes are similar to UDGs in all properties except for being, by definition, smaller and having higher surface brightness. We find that UDGs and NUDGes show similar behaviours in their GC populations, with the most metal-poor galaxies hosting consistently more GCs on average. This suggests that GC content may provide an effective way to distinguish extreme galaxies within the low surface brightness regime alongside traditional parameters like size and surface brightness. We confirm previous results using clustering algorithms that UDGs split into two main classes, which might be associated with the formation pathways of a puffy dwarf and a failed galaxy. The clustering applied to the UDGs+NUDGes dataset yields an equivalent result. The difference in mass contained in the GC system suggests that galaxies in different environments have not simply evolved from one another but may have formed through distinct processes.

Stratified distributional analysis-a novel perspective on RT distributions.

Response times and their distributions serve as a powerful lens into cognitive processes. We present a novel statistical methodology called stratified distributional analysis (SDA) to quantitatively assess how key determinants of response times (word frequency and length) shape their distributions. Taking advantage of the availability of millions of lexical decision response times in the English Lexicon Project and the British Lexicon Project, we made important advances into the theoretical issue of linking response times and word frequency by analysing RT distributions as a function of word frequency and word length. We tested these distributions against the lognormal, Wald, and gamma distributions and three measures of word occurrence (word form frequencies obtained from subtitles and contextual diversity as operationalised as discourse contextual diversity and user contextual diversity). We found that the RT distributions were best described by a lognormal distribution across both megastudies when word occurrence was quantified by a contextual diversity measure. The link between the lognormal distribution and its generative process highlights the power of SDA in elucidating mechanisms that govern the generation of RTs through the fitting of probability distributions. Using a hierarchical Bayesian framework, SDA yielded posterior distributions for the distributional parameters at the single-participant level, enabling probabilistic predictions of response times as a function of word frequency and word length, which has the potential to serve as a diagnostic tool to uncover idiosyncratic features of word processing. Crucially, while we applied our parsimonious methodology to lexical decision response times, it is applicable to a variety of tasks such as word-naming and eye-tracking data.

Self-regulated growth of galaxy sizes along the star-forming main sequence

We present a systematic analysis of the spatially-resolved star formation histories (SFHs) using Hubble Space Telescope imaging data of ∼997, intermediate redshifts 0.5≤z≤2.0 galaxies from GOODS-S field, with stellar mass range 9.8≤logM⋆/M⊙≤11.5. We estimate the SFHs in three spatial regions (central region within the half-mass radii R50s, outskirts between 1−3R50s, and the whole galaxy) using pixel-by-pixel spectral-energy distribution (SED) fitting, assuming exponentially declining tau model in individual pixels. The reconstructed SFHs are then used to derive and compare the physical properties such as specific star-formation rates (sSFRs), mass-weighted ages (t 50), and the half mass-radii to get insights on the interplay between the structure and star-formation in galaxies. The correlation of sSFRs ratio of the centre and outskirts with the distance from the main sequence (MS) indicates that galaxies on the upper envelope of the MS tend to grow outside-in, building up their central regions, while those below the MS grow inside-out, with more active star-formation in the outskirts. The findings suggest a self-regulating process in galaxy size growth when they evolve along the MS. Our observations are consistent with galaxies growing their inner bulge and outer disc regions, where they appear to oscillate about the average MS in cycles of central gas compaction, which leads to bulge growth, and subsequent central depletion possibly due to feedback from the starburst resulting in more star formation towards the outskirts from newly accreted gas.

Distribution Fitting for Combating Mode Collapse in Generative Adversarial Networks.

Mode collapse is a significant unsolved issue of generative adversarial networks (GANs). In this work, we examine the causes of mode collapse from a novel perspective. Due to the nonuniform sampling in the training process, some subdistributions may be missed when sampling data. As a result, even when the generated distribution differs from the real one, the GAN objective can still achieve the minimum. To address the issue, we propose a global distribution fitting (GDF) method with a penalty term to confine the generated data distribution. When the generated distribution differs from the real one, GDF will make the objective harder to reach the minimal value, while the original global minimum is not changed. To deal with the circumstance when the overall real data is unreachable, we also propose a local distribution fitting (LDF) method. Experiments on several benchmarks demonstrate the effectiveness and competitive performance of GDF and LDF.

Fitting Probability Distributions and Statistical Trend Analysis of Rainfall of Agro-climatic Zone of West Bengal

This research aimed to identify the most appropriate probability distribution for modeling average monthly rainfall in the agro-climatic zones of West Bengal and to detect any trends in this data. The study utilized historical rainfall data spanning 51 years (1970-2020) obtained from the IMD in Pune. To determine the best-fitting distribution and assess trends, 23 different probability distributions were employed, with the Mann-Kendall test and Sen’s slope estimator used for trend analysis. Goodness-of-fit tests, including the Kolmogorov-Smirnov, Anderson-Darling, and Chi-square tests, were employed to determine the most suitable distribution. The findings indicated that the Generalized Extreme Value, Gamma, and Lognormal (3-parameter) distributions were the best fits for two specific districts. The monthly rainfall distributions can be effectively used for predicting future monthly rainfall events in the region. The Mann-Kendall test revealed an increasing trend in rainfall for Kalimpong and Nadia Districts and a decreasing trend for Malda District.

The mass distribution of behind-armor debris generated during the normal penetration of an explosively formed projectile on rolled homogeneous armor steel

Abstract To obtain the mass distribution law of behind-armor debris(BAD) produced by EFP vertically penetrating armored steel, the numerical simulation calculation of EFP vertically penetrating targets with different thicknesses (30mm ∼ 70mm) at different impact velocities (1600m/s ∼ 2000m/s) was carried out by using the numerical simulation method verified by experiments. Several classical natural fragment mass distribution models are used to study the mass distribution of the BAD generated by EFP and the target plate. The results show that the classical Mott formula is not suitable for describing the mass-quantity distribution of the BAD generated by warhead penetration, while the two-parameter Weibull distribution is a good fit for the mass distribution of the BAD, but both of them depend on the total number of fragments, and it is impossible to ensure that small debris is completely collected in the test. Therefore, it is often impossible to determine the total number of debris. In contrast, the Held distribution does not depend on the total number of debris, and the correlation coefficient of fitting results for the mass distribution of BAD is closest to 1, indicating that the Held distribution is the most suitable for describing the mass distribution of BAD. According to the variation of the characteristic parameter of Held distribution with the thickness of the target plate and EFP impact velocity, the mathematical expression between the characteristic parameter of Held formula and the dimensionless initial condition is established. Based on the Held distribution, a prediction model of the mass distribution of the BAD is established, which takes into account the impact velocity of EFP and the thickness of the target plate. The model estimation is in good agreement with the simulation results, which proves the accuracy of the established model.

The Star-forming Main Sequence in JADES and CEERS at z > 1.4: Investigating the Burstiness of Star Formation

We have used public JWST/NIRSpec and JWST/NIRCam observations from the CEERS and JADES surveys in order to analyze the star-forming main sequence (SFMS) over the redshift range 1.4 ≤ z < 7. We calculate the star formation rates (SFRs) of the galaxy sample using three approaches: Balmer line luminosity, spectral energy distribution (SED) fitting, and UV luminosity. We find a larger degree of scatter about the SFMS using the Balmer-based SFRs compared to the UV-based SFRs. Because these SFR indicators are sensitive to star formation on different timescales, the difference in scatter may be evidence of bursty star formation histories in the early Universe. We additionally compare the Hα-to-UV luminosity ratio (L(Hα)/ν L ν,1600) for individual galaxies in the sample and find that 29%–52% of the ratios across the sample are poorly described by predictions from a smooth star formation history. Measuring the burstiness of star formation in the early Universe has multiple significant implications, such as deriving accurate physical parameters from SED fitting, explaining the evolution of the UV luminosity function, and providing constraints for subgrid models of feedback in simulations of galaxy formation and evolution.

Radial properties of dust in galaxies: Comparison between observations and isolated galaxy simulations

We study the importance of several processes that influence the evolution of dust and its grain size distribution on spatially resolved scales in nearby galaxies. Here, we compiled several multi-wavelength observations for the nearby galaxies NGC 628 (M74), NGC 5457 (M101), NGC 598 (M33), and NGC 300. We applied spatially resolved spectral energy distribution (SED) fitting to the latest iteration of infrared data to get constraints on the galaxy dust masses and the small-to-large grain abundance ratio (SLR). We separated each galaxy into radial rings and obtained the radial profiles of the properties mentioned above. For comparison, we took the radial profiles of the stellar mass and gas mass surface density for NGC 628 combined with its metallicity gradient in the literature to calibrate a single-galaxy simulation using the GADGET4-OSAKA code. The simulations include a parametrization to separate the dense and diffuse phases of the ISM where different dust-evolution mechanisms are in action. We find that our simulation can reproduce the radial profile of dust mass surface density but overestimates the SLR in NGC 628. Changing the dust-accretion timescale has little impact on the dust mass or SLR, as most of the available metals are accreted onto dust grains at early times (&lt; 3 Gyr), except in the outer regions of the galaxy where the metallicity is below 2 × 10−3. This suggests we can only constrain the accretion timescale of galaxies at extremely low metallicities where accretion still competes with other mechanisms controlling the dust budget. The overestimation of the SLR likely results from (i) overly efficient shattering processes in the diffuse interstellar medium (ISM), which were calibrated to reproduce Milky Way-type galaxies and/or (ii) our use of a diffuse and dense gas density subgrid model that does not entirely capture the intricacies of the small-scale structure present in NGC 628. We conclude that future modeling efforts will need to focus on improving the subgrid recipes to mimic the multi-phase gas distribution in galaxies before the efficiency of dust evolution processes can be calibrated for galaxies other than the Milky Way.