Pith. sign in

REVIEW 4 major objections 5 minor 1 cited by

Modelling and prediction of the wildfire data using fractional Poisson process

T0 review · 4 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read The paper argues that California wildfire occurrences are dependent events with fractional parameter β ≈ 0.8, and that a fractional Poisson process predicts the next fire dates about 90% more accurately than the classical Poisson process.

desk verdict The fPP application to wildfires is new, but the real-data analysis is unsound: two parameters estimated from one count, and a 90% prediction improvement from a single simulated draw. read the letter →

arxiv 2411.13995 v1 pith:OS5A6HNE submitted 2024-11-21 stat.AP

Sudeep R. Bapat , Aditya Maheshwari This is my paper · ORCID
classification stat.AP
keywords wildfiremodellingfractionalPoissonprocesslongmemorymethodofmomentsmaximumlikelihoodMittag-LefflerdistributionCaliforniawildfiresforecasting
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper argues that wildfire occurrences in California between June 2019 and April 2023 should be modeled by a fractional Poisson process rather than a classical Poisson process. The fractional model allows past fires to influence the timing of future fires, and the authors estimate the fractional parameter at 0.8, which they read as evidence of long-memory dependence. On the same data, their fitted fractional model predicts the next ten fire dates with roughly a 90 percent smaller mean-squared error than the Poisson model. If correct, the result would replace the standard independence assumption with a concrete dependence parameter and improve operational forecasts.

What carries the argument

The central object is the fractional Poisson process (fPP), a counting process whose waiting times between events follow a Mittag-Leffler distribution; the fractional order $\beta \in (0,1]$ controls deviation from Poisson behavior, with $\beta = 1$ recovering the exponential interarrival times of the classical Poisson process. The argument is carried by two moment identities: the mean count $E[N_\beta(t)] = q t^\beta$ and a variance formula involving the $\beta$ function, which the method-of-moments procedure equates to an observed count and its square to solve for $\lambda$ and $\beta$. Once estimated, the model generates future interarrival times through a stochastic representation for Mittag-Leffler variables, enabling the date-by-date forecast comparison.

What would settle it

Refit the full set of 146 recorded interarrival times with a maximum-likelihood estimator for a Mittag-Leffler waiting-time distribution, and compute a confidence interval for $\beta$; if the interval covers 1, the dependence claim collapses. Alternatively, repeat the ten-step forecast on many independently simulated draws from the fitted fractional process and compare average error to the Poisson model; if the 90 percent reduction does not persist, the prediction claim fails.

Watch

Extended reading notes

Core claim

The central claim is that a two-parameter fractional Poisson process, with rate $\lambda^* = 0.69$ and fractional order $\beta^* = 0.8$, describes California wildfire occurrence better than a one-parameter Poisson process with estimated rate 0.28. Because $\beta$ is below 1, the fitted model says wildfire interarrival times are Mittag-Leffler distributed rather than exponential, so events are not independent: past occurrences statistically affect later ones. The paper supports this by solving the process's first two theoretical moment equations against a single observed count of 56 fires in the first 200 days, and then reports a goodness-of-fit test that favors the fractional process. It further claims a 90 percent reduction in prediction error over the Poisson model when forecasting ten future fire dates. The paper frames both findings as evidence that wildfire events carry long memory.

Load-bearing premise

The entire analysis rests on treating one observed number—56 fires within the first 200 days, and its square—as two sample moments that can uniquely determine both $\lambda$ and $\beta$, with no sampling distribution or uncertainty attached.

Editorial extensions

If this is right

  • Wildfire occurrence in California should not be treated as independent events; any count or forecast model that assumes Poisson arrivals will misstate the clustering.
  • Because the fitted fractional parameter is 0.8, the dependence is strong enough to matter for practical prediction: the fitted model places the next ten fire dates much closer to observed dates than the Poisson model.
  • The method-of-moments and maximum-likelihood estimators introduced for the two fPP parameters can be used on other disaster-event timelines, not just wildfires.
  • The long-memory finding would justify developing early-warning systems that use recent fire activity as an input, rather than treating each fire as a fresh random event.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A fairer test of the 90 percent claim would average prediction error over many simulated forecast origins, since the reported comparison uses a single random draw of ten future interarrival times.
  • The single-count calibration provides no confidence interval for $\beta$, so a bootstrap over resampled interarrival times could show whether 0.8 is meaningfully different from 1.
  • The estimated $\beta < 1$ may partly absorb seasonal clustering rather than genuine long memory; fitting a seasonal Poisson or self-exciting process would separate those mechanisms.
  • If the moment equations are ill-identified from one count, a Bayesian fit using the observed 146 waiting times would give a more direct estimate of $\beta$ and a built-in uncertainty band.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper proposes the fractional Poisson process (fPP) as a model for wildfire occurrences in California between June 2019 and April 2023. It introduces method-of-moments and maximum-likelihood estimation approaches for the fPP parameters, validates them in simulation, and then applies the method-of-moments to a single observed count N(200)=56, obtaining λ*=0.69 and β*=0.8. The authors interpret β*=0.8 as evidence of dependence/long memory in wildfire events. They then generate ten fPP and ten Poisson interarrival times, compare the resulting predicted occurrence times with the actual next ten occurrence times, and report a roughly 90% reduction in MSE/MAD relative to the Poisson process.

Significance. If the claims were reliable, the finding that California wildfire occurrences exhibit long-range dependence and can be predicted far better by a fractional Poisson process than by a homogeneous Poisson process would be practically relevant for wildfire risk planning. The paper also provides a simulation comparison of two estimation methods for the fPP, which could serve as a reference if the methods were properly validated. However, the central applied conclusions rest on two very fragile statistical steps: estimating two parameters from a single realized count with no uncertainty quantification, and comparing forecasts on the basis of a single simulated interarrival sequence. Neither step supports the strength of the claims made in the abstract. The paper does not provide code, data, or a reproducibility statement, which further limits verification of the simulation-based results.

major comments (4)
  1. [§5.2, Eqs. (4)–(5)] The parameters λ and β are estimated by solving equations (4) and (5) with nt = Nβ(200) = 56 and nt² = 56², i.e., from a single realized count. A single count has no sampling distribution, and treating nt and nt² as sample moments provides no basis for inference. No standard errors, confidence intervals, sensitivity analysis, or profile likelihood is reported, so the estimate β*=0.8 cannot be used to claim that β differs from 1, let alone that it 'proves' dependence. Moreover, the full interarrival/occurrence-time data (146 occurrence days) are available but are discarded by the count reduction; using the full data would be needed to identify the dependence parameter reliably.
  2. [§6, Tables 3–4] The reported 90% prediction-error reduction is computed from one simulated sequence of ten fPP interarrival times and one simulated PP sequence. Because the fPP interarrival distribution is heavy-tailed, a single Monte Carlo draw can be unrepresentative; the MSE values (526.14 vs. 39562.1) are realized values with no measure of variability. A proper comparison would report the mean and spread of the prediction error over many simulated sequences (or a predictive distribution) and would propagate the uncertainty in the parameter estimates. Additionally, the 'time of occurrence' values in Table 3 are consistent with adding the simulated interarrival times to an origin at day 146—the total number of occurrence days in the full dataset—but the paper never states that the 56th occurrence happens on day 146, making the forecast construction ambiguous.
  3. [§3, MoM simulation] The simulation study solves equations (4)–(5) separately for each of 1000 simulated paths (each path yields a single count), producing per-path estimates λ*_j, β*_j that are then averaged. This is not the standard method of moments, which would equate the sample mean and second moment over the 1000 independent counts to the theoretical moments in (2) and (3). The per-path procedure may produce estimates even when a single count is inconsistent with the two-moment system, and the reported bias and MSE describe that ad-hoc per-path estimator rather than a proper MoM estimator. Since the real-data application in §5.2 follows the same single-count logic, the simulation does not validate the step actually used.
  4. [§2.2, initial condition] The initial condition for the fPP pmf is stated as 'pβ(n, 0) = 0 if n = 0 and is zero if n ≥ 1', which gives pβ(0,0)=0. The correct condition is pβ(0,0)=1 and pβ(n,0)=0 for n≥1. As written, the pmf (1) cannot be consistent with a proper probability distribution at t=0. This is a basic definitional error that affects the likelihood and the moment equations derived later.
minor comments (5)
  1. [§5.2] The sentence 'Using the method of moments equations, (5) and (6)' should refer to equations (4) and (5); equation (6) is a bias formula.
  2. [§5.3] The statement 'Finding the MLE is hence not possible from a single sample value' is imprecise: the likelihood function is still defined for a single count and can in principle be maximized, though parameter identifiability from one observation is poor. The authors should explain why MLE is infeasible or unstable rather than impossible.
  3. [§6, Table 4] The phrase 'MSE (as defined in Eq. (9))' is a dangling reference; equation (9) is the observed information matrix, and no MSE formula appears in Section 6.
  4. [§5.1–5.2, Figure 6] The description of the ECDF comparison is unclear about how the ECDFs for the two fitted processes are constructed (e.g., by simulating many sample paths and pooling counts, or by using a theoretical distribution). Without this detail, the reported Kolmogorov-Smirnov p-values (0.1761 and 0.00034) are not reproducible, and the fact that parameters were estimated from the same data should be addressed when interpreting those p-values.
  5. [§4, Eq. (8)] In the likelihood expression (8), the threshold t appears without being indexed or declared as a known constant; the notation should be made explicit (e.g., L(λ, β; t)) so that the dependence on t is clear.

Circularity Check

0 steps flagged · score 2.0 of 10

No substantial circularity: the fitted parameters are estimated from the first 200 days and the prediction target is out-of-sample, so the 90% error reduction is not forced by construction; the only self-citation is background and not load-bearing.

full rationale

The central derivation chain is not circular. The fPP parameters λ*=0.69 and β*=0.8 are obtained in Section 5.2 by solving the method-of-moments equations (4)-(5) using the observed single count Nβ(200)=56. The future occurrence times used in the Section 6 comparison (Table 3) are the actual observed times after the 56th occurrence, which were not used in this estimation; hence the claimed 90% reduction in prediction error is an out-of-sample empirical comparison, not a quantity that is equal to the fitting equations by construction. The long-memory interpretation relies on the cited mathematical result of Maheshwari and Vellaisamy (2016) [20] that increments of the fPP have long-range dependence for β<1; this is an external theorem, also supported by [3] and [18], and it is not the source of the fitted values. The self-citation is thus minor and not load-bearing. The paper's real weaknesses are statistical rather than circular: a single count provides no sampling distribution or uncertainty for λ* and β*; the data contain many interarrival times that are unused in estimation; and the prediction comparison is based on one unseeded simulated draw of the fPP interarrival times. These issues undermine the strength of the dependence and prediction claims but do not make the derivation circular.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The central claim depends on fitted values λ*=0.69 and β*=0.8, a hand-chosen threshold t=200, and a truncation order k=49 that the paper sets because 'it was observed that for k>49, the summand is negligible'. The model identification rests on the assumption that a single count N(200)=56 carries enough information for two parameters, which is an ad hoc premise of the paper. Background mathematical facts about the fPP pmf and moments are inherited from the cited literature. No new entities are postulated.

free parameters (5)
  • fPP rate parameter λ* = 0.69
    Solved from equations (4) and (5) using a single observed count N(200)=56; a hand-fit value, not an estimator with uncertainty.
  • fractional long-memory parameter β* = 0.8
    Same single-observation solve; used to claim dependence of wildfire events.
  • PP rate parameter λ* = 0.28
    Fitted to the same single count N(200)=56 under the standard Poisson assumption.
  • Threshold t = 200 days
    Chosen by hand in Sections 5.2 and 6; the fitted counts Nβ(t)=56 depend on this choice.
  • Truncation order k in the likelihood/pmf sum = 49
    Set because the summand becomes negligible for k>49 (Section 4); affects both MLE and pmf evaluations.
assumptions (5)
  • standard math The fPP pmf in Eq. (1) and moment formulas in Eqs. (2)-(3) are correct as stated
    Taken from Laskin (2003) and Beghin-Orsingher (2009); background literature.
  • domain assumption The inter-arrival times of the fPP are generated by the Kanter (1975) formula in Section 6
    The formula is stated without derivation; it is a standard representation for stable laws, and its equivalence to the Mittag-Leffler inter-arrival distribution of the fPP is not shown.
  • domain assumption Wildfire occurrence records from the NOAA Storm Events Database for California June 2019-April 2023 are complete and consistently defined
    The dataset is external and the extraction is not fully specified; the count N(200)=56 is taken as ground truth.
  • ad hoc to paper The fPP is an appropriate model for a single observed count and one can identify two parameters from it
    The paper's MoM approach in Section 5.2 treats one count as two sample moments; no statistical justification is given.
  • domain assumption A point estimate β*=0.8 implies long-memory dependence in the data
    The paper cites literature that fPP increments have LRD for certain β, but does not establish a test or confidence region for β=0.8.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Modelling and prediction of the wildfire data using fractional Poisson process." pith.science (2026). https://pith.science/paper/OS5A6HNE

@misc{pith2026241113995,
  author       = {Pith},
  title        = {Pith review of: Modelling and prediction of the wildfire data using fractional Poisson process},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OS5A6HNE}},
  note         = {Machine review of arXiv:2411.13995}
}
read the original abstract

Modelling wildfire events has been studied in the literature using the Poisson process, which essentially assumes the independence of wildfire events. In this paper, we use the fractional Poisson process to model the wildfire occurrences in California between June 2019 - April 2023 and predict the wildfire events that explains the underlying memory between these events. We introduce method of moments and maximum likelihood estimate approaches to estimate the parameters of the fractional Poisson process, which is an alternative to the method proposed by Cahoy (2010). We obtain the estimates of the fractional parameter as 0.8, proving that the wildfire events are dependent. The proposed model has reduced prediction error by 90\% compared to the classical Poisson process model.

Figures

Figures reproduced from arXiv: 2411.13995 by the authors.

Figure 1
Figure 1. Estimates for λ and β when the true values are λ = 2, β = 0.8. 4 Parameter estimation - Maximum likelihood Assume for a fixed m, nt1, nt2, ..., ntm be the observed data, where nti, i = 1, 2, ..., m denotes the number of occurrences of the fPP which are less than some threshold (say t), from the i th sample path. Then, the likelihood function can be written down as follows, L(λ, β) = Ym i=1 ( (λtβ ) nti nti! X∞ k=0 (… view at source ↗
Figure 2
Figure 2. gives the trajectories of both the parameter estimates. One can see that the estimates are located close to their actual values, with very few outliers [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Normal Q-Q plots for λˆ (left) and βˆ (right). 5 Practical data analysis Modeling wildfire occurrences across the globe has always been a challenge, mainly due to the complexity of such a data. The unpredictability of climate driven wildfires, along with their increasing size and coverage, makes it difficult to come up with a suitable model which can capture the behaviour of its patterns. In this paper, we will appl… view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: California wildfire occurrences over three years. Provided by “OpenStreetMap” [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 5
Figure 5. Figure 5: Scatterplot (left) and histogram (right) of the times from origin, in days. [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]
Figure 6
Figure 6. Figure 6: Sample ECDFs of the actual data and the two processes [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]
Figure 7
Figure 7. Figure 7: Predicted time of occurrences with the actual data [PITH_FULL_IMAGE:figures/full_fig_p013_7.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Fractional counting process at L\'evy times and its applications

    math.PR 2024-12 conditional novelty 4.0 of 10

    A Lévy-subordinated fractional counting process is defined and its distributional properties, compound variants, Bell-polynomial connections, and a shock model are derived.

Reference graph

Works this paper leans on

41 extracted references · 41 canonical work pages · cited by 1 Pith paper

  1. [1]

    Aguilera, T

    R. Aguilera, T. Corringham, A. Gershunov, and T. Benmarhnia. Wildfire smoke impacts respiratory health more than fine particles from other sources: observational evidence from southern california. Nature communications, 12(1):1493, 2021

    work page 2021

  2. [2]

    Beghin and E

    L. Beghin and E. Orsingher. Fractional Poisson processes and related planar random motions. Electron. J. Probab., 14:no. 61, 1790–1827, 2009

    work page 2009

  3. [3]

    Biard and B

    R. Biard and B. Saussereau. Fractional Poisson process: long-range dependence and applications in ruin theory. J. Appl. Probab. , 51(3):727–740, 2014

    work page 2014

  4. [4]

    Blender, C

    R. Blender, C. C. Raible, and F. Lunkeit. Non-exponential return time distributions for vorticity extremes explained by fractional poisson processes. Quarterly Journal of the Royal Meteorological Society, 141(686):249–257, 2015

    work page 2015

  5. [5]

    Boubeta, M

    M. Boubeta, M. J. Lombard ´ ıa, M. Marey-P´ erez, and D. Morales. Poisson mixed models for predicting number of fires. Int. J. Wildland Fire , 28(3):237, 2019. 14

    work page 2019

  6. [6]

    Boubeta, M

    M. Boubeta, M. J. Lombard ´ ıa, M. F. Marey-P´ erez, and D. Morales. Prediction of forest fires occurrences with area-level poisson mixed models. J. Environ. Manage. , 154:151–158, May 2015

    work page 2015

  7. [7]

    D. O. Cahoy, V. V. Uchaikin, and W. A. Woyczynski. Parameter estimation for frac- tional Poisson processes. J. Statist. Plann. Inference , 140(11):3106–3120, 2010

    work page 2010

  8. [8]

    Z. Ding, C. W. Granger, and R. F. Engle. A long memory property of stock market returns and a new model. Journal of Empirical Finance , 1(1):83 – 106, 1993

    work page 1993

Show all 41 references
  1. [9]

    Doukhan, G

    P. Doukhan, G. Oppenheim, and M. S. Taqqu, editors. Theory and applications of long-range dependence. Birkh¨ auser Boston, Inc., Boston, MA, 2003

    2003

  2. [10]

    C. A. Graff, S. R. Coffield, Y. Chen, E. Foufoula-Georgiou, J. T. Randerson, and P. Smyth. Forecasting daily wildfire activity using poisson regression. IEEE Trans. Geosci. Remote Sens. , 58(7):4837–4851, July 2020

    2020

  3. [11]

    Jiang, Q

    Y. Jiang, Q. Zhuang, and D. Mandallaz. Modeling large fire frequency and burned area in canadian terrestrial ecosystems with poisson models. Environ. Model. Assess. , 17(5):483–493, Oct. 2012

    2012

  4. [12]

    G. Jumarie. Fractional master equation: non-standard analysis and Liouville-Riemann derivative. Chaos Solitons Fractals, 12(13):2577–2587, 2001

    2001

  5. [13]

    M. Kanter. Stable densities under change of scale and total variation inequalities. Ann. Probability, 3(4):697–707, 1975

    1975

  6. [14]

    Karagiannis, M

    T. Karagiannis, M. Molle, and M. Faloutsos. Long-range dependence ten years of internet traffic modeling. Internet Computing, IEEE , 8(5):57–64, 2004

    2004

  7. [15]

    A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo. Theory and applications of fractional differential equations, volume 204 of North-Holland Mathematics Studies . Elsevier Sci- ence B.V., Amsterdam, 2006

    2006

  8. [16]

    Kumar, N

    A. Kumar, N. Leonenko, and A. Pichler. Fractional risk process in insurance. Math Finan Econ, 06 2019

    2019

  9. [17]

    N. Laskin. Fractional Poisson process. Commun. Nonlinear Sci. Numer. Simul. , 8(3- 4):201–213, 2003. Chaotic transport and complexity in classical and quantum dynamics

    2003

  10. [18]

    N. N. Leonenko, M. M. Meerschaert, R. L. Schilling, and A. Sikorskii. Correlation structure of time-changed l´ evy processes.Commun. Appl. Ind. Math. , 2014

    2014

  11. [19]

    R. R. Linhares. Fractional poisson process: Long-range dependence in dna sequences. Model Assisted Statistics and Applications , 18(1):33–43, 2023

    2023

  12. [20]

    Maheshwari and P

    A. Maheshwari and P. Vellaisamy. On the long-range dependence of fractional poisson and negative binomial processes. J. Appl. Probab. , 53:989–1000, 2016. 15

    2016

  13. [21]

    Mainardi, R

    F. Mainardi, R. Gorenflo, and E. Scalas. A fractional generalization of the Poisson processes. Vietnam J. Math. , 32:53–64, 2004

    2004

  14. [22]

    Mainardi, R

    F. Mainardi, R. Gorenflo, and A. Vivoli. Beyond the Poisson renewal process: a tutorial survey. J. Comput. Appl. Math. , 205(2):725–735, 2007

    2007

  15. [23]

    Malik, M

    A. Malik, M. R. Rao, N. Puppala, P. Koouri, V. A. K. Thota, Q. Liu, S. Chiao, and J. Gao. Data-driven wildfire risk prediction in northern california. Atmosphere, 12(1):109, 2021

    2021

  16. [24]

    Mandallaz and R

    D. Mandallaz and R. Ye. Prediction of forest fires with poisson models. Canadian Journal of Forest Research, 27(10):1685–1694, 1997

    1997

  17. [25]

    A. Pagan. The econometrics of financial markets. Journal of Empirical Finance, 3(1):15 – 102, 1996

    1996

  18. [26]

    Papakosta and D

    P. Papakosta and D. Straub. Probabilistic prediction of daily fire occurrence in the mediterranean with readily available spatio-temporal data. IForest, 10(1):32–40, Feb. 2017

    2017

  19. [27]

    Pastor, L

    E. Pastor, L. Z´ arate, E. Planas, and J. Arnaldos. Mathematical models and calculation systems for the study of wildland fire behaviour. Progress in Energy and Combustion Science, 29(2):139–153, 2003

    2003

  20. [28]

    Paxson and S

    V. Paxson and S. Floyd. Wide area traffic: the failure of poisson modeling. IEEE/ACM Transactions on Networking, 3(3):226–244, Jun 1995

    1995

  21. [29]

    J. J. Quinlan, C. D ´ ıaz-Avalos, and R. H. Mena. Modeling wildfires via marked spatio- temporal poisson processes. Environ. Ecol. Stat. , 28(3):549–565, Sept. 2021

    2021

  22. [30]

    O. N. Repin and A. I. Saichev. Fractional Poisson law. Radiophys. and Quantum Electronics, 43(9):738–741 (2001), 2000

    2001

  23. [31]

    V. K. Rohatgi and A. M. E. Saleh. An introduction to probability and statistics . John Wiley & Sons, 2015

    2015

  24. [32]

    D. L. Swain. A shorter, sharper rainy season amplifies california wildfire risk. Geophys- ical Research Letters, 48(5):e2021GL092843, 2021

    2021

  25. [33]

    Varotsos and D

    C. Varotsos and D. Kirk-Davidoff. Long-memory processes in ozone and temperature variations at the region 60 ◦s-60 ◦n. Atmospheric Chemistry and Physics , 6(12):4093– 4100, 2006

    2006

  26. [34]

    Vellaisamy and A

    P. Vellaisamy and A. Maheshwari. Fractional negative binomial and Polya processes. Probab. Math. Statist. , 38(1):77–101, 2018

    2018

  27. [35]

    Wang and Z.-X

    X.-T. Wang and Z.-X. Wen. Poisson fractional processes. Chaos Solitons Fractals , 18(1):169–177, 2003. 16

    2003

  28. [36]

    Wang, Z.-X

    X.-T. Wang, Z.-X. Wen, and S.-Y. Zhang. Fractional Poisson process. II. Chaos Solitons Fractals, 28(1):143–147, 2006

    2006

  29. [37]

    Wang, S.-Y

    X.-T. Wang, S.-Y. Zhang, and S. Fan. Nonhomogeneous fractional Poisson processes. Chaos Solitons Fractals, 31(1):236–241, 2007

    2007

  30. [38]

    Westerling, B

    A. Westerling, B. Bryant, H. K. Preisler, T. P. Holmes, H. Hidalgo, T. Das, and S. R. Shrestha. Climate change and growth scenarios for california wildfire. Climatic Change, 109:445–463, 2011

    2011

  31. [39]

    A. L. Westerling and B. Bryant. Climate change and wildfire in california. Climatic Change, 87:231–249, 2008

    2008

  32. [40]

    Willinger and V

    W. Willinger and V. Paxson. Where mathematics meets the internet. Notices Amer. Math. Soc., 45(8):961–970, 1998

    1998

  33. [41]

    Y. Xiao, X. Zhang, and P. Ji. Modeling forest fire occurrences using count-data mixed models in qiannan autonomous prefecture of guizhou province in china. PLoS One , 10(3):e0120621, Mar. 2015. 17

    2015

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.