feat: statistics tests

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+     <use xlink:href="#ArialMT-6e" transform="translate(444.580078 0)"/>
+     <use xlink:href="#ArialMT-20" transform="translate(500.195312 0)"/>
+     <use xlink:href="#ArialMT-62" transform="translate(527.978516 0)"/>
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+     <use xlink:href="#ArialMT-65" transform="translate(816.992188 0)"/>
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+     <use xlink:href="#ArialMT-6f" transform="translate(928.222656 0)"/>
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+     <use xlink:href="#ArialMT-79" transform="translate(1017.138672 0)"/>
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+   <g id="matplotlib.axis_4"/>
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+   <g id="text_6">
+    <!-- Male -->
+    <g style="fill: #262626" transform="translate(368.374913 415.543883) scale(0.1 -0.1)">
+     <defs>
+      <path id="ArialMT-4d" d="M 475 0 
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+     <use xlink:href="#ArialMT-4d"/>
+     <use xlink:href="#ArialMT-61" transform="translate(83.300781 0)"/>
+     <use xlink:href="#ArialMT-6c" transform="translate(138.916016 0)"/>
+     <use xlink:href="#ArialMT-65" transform="translate(161.132812 0)"/>
+    </g>
+   </g>
+   <g id="text_7">
+    <!-- 61.6% -->
+    <g style="fill: #262626" transform="translate(439.1278 391.471734) scale(0.1 -0.1)">
+     <defs>
+      <path id="ArialMT-31" d="M 2384 0 
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+     <use xlink:href="#ArialMT-36"/>
+     <use xlink:href="#ArialMT-31" transform="translate(55.615234 0)"/>
+     <use xlink:href="#ArialMT-2e" transform="translate(111.230469 0)"/>
+     <use xlink:href="#ArialMT-36" transform="translate(139.013672 0)"/>
+     <use xlink:href="#ArialMT-25" transform="translate(194.628906 0)"/>
+    </g>
+   </g>
+   <g id="text_8">
+    <!-- Female -->
+    <g style="fill: #262626" transform="translate(668.374802 309.62643) scale(0.1 -0.1)">
+     <defs>
+      <path id="ArialMT-46" d="M 525 0 
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+     <use xlink:href="#ArialMT-46"/>
+     <use xlink:href="#ArialMT-65" transform="translate(61.083984 0)"/>
+     <use xlink:href="#ArialMT-6d" transform="translate(116.699219 0)"/>
+     <use xlink:href="#ArialMT-61" transform="translate(200 0)"/>
+     <use xlink:href="#ArialMT-6c" transform="translate(255.615234 0)"/>
+     <use xlink:href="#ArialMT-65" transform="translate(277.832031 0)"/>
+    </g>
+   </g>
+   <g id="text_9">
+    <!-- 38.4% -->
+    <g style="fill: #262626" transform="translate(590.942228 333.698578) scale(0.1 -0.1)">
+     <defs>
+      <path id="ArialMT-33" d="M 269 1209 
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+     <use xlink:href="#ArialMT-33"/>
+     <use xlink:href="#ArialMT-38" transform="translate(55.615234 0)"/>
+     <use xlink:href="#ArialMT-2e" transform="translate(111.230469 0)"/>
+     <use xlink:href="#ArialMT-34" transform="translate(139.013672 0)"/>
+     <use xlink:href="#ArialMT-25" transform="translate(194.628906 0)"/>
+    </g>
+   </g>
+   <g id="text_10">
+    <!-- Distribution by Sex -->
+    <g style="fill: #262626" transform="translate(479.192201 184.796141) scale(0.12 -0.12)">
+     <defs>
+      <path id="ArialMT-78" d="M 47 0 
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+     <use xlink:href="#ArialMT-69" transform="translate(72.216797 0)"/>
+     <use xlink:href="#ArialMT-73" transform="translate(94.433594 0)"/>
+     <use xlink:href="#ArialMT-74" transform="translate(144.433594 0)"/>
+     <use xlink:href="#ArialMT-72" transform="translate(172.216797 0)"/>
+     <use xlink:href="#ArialMT-69" transform="translate(205.517578 0)"/>
+     <use xlink:href="#ArialMT-62" transform="translate(227.734375 0)"/>
+     <use xlink:href="#ArialMT-75" transform="translate(283.349609 0)"/>
+     <use xlink:href="#ArialMT-74" transform="translate(338.964844 0)"/>
+     <use xlink:href="#ArialMT-69" transform="translate(366.748047 0)"/>
+     <use xlink:href="#ArialMT-6f" transform="translate(388.964844 0)"/>
+     <use xlink:href="#ArialMT-6e" transform="translate(444.580078 0)"/>
+     <use xlink:href="#ArialMT-20" transform="translate(500.195312 0)"/>
+     <use xlink:href="#ArialMT-62" transform="translate(527.978516 0)"/>
+     <use xlink:href="#ArialMT-79" transform="translate(583.59375 0)"/>
+     <use xlink:href="#ArialMT-20" transform="translate(633.59375 0)"/>
+     <use xlink:href="#ArialMT-53" transform="translate(661.376953 0)"/>
+     <use xlink:href="#ArialMT-65" transform="translate(728.076172 0)"/>
+     <use xlink:href="#ArialMT-78" transform="translate(783.691406 0)"/>
+    </g>
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+ </g>
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assets/identified_category_distribution.csv

@@ -1,13 +1,13 @@
-province,compose,simple
+compose,simple
-AUTRES,0.2062165520477412,0.7937834479522587
+0.2062165520477412,0.7937834479522587
-BANDUNDU,0.6269061385346485,0.3730938614653515
+0.6269061385346485,0.3730938614653515
-BAS-CONGO,0.09081330148566008,0.90918669851434
+0.09081330148566008,0.90918669851434
-EQUATEUR,0.12423822403788959,0.8757617759621105
+0.12423822403788959,0.8757617759621105
-KASAI-OCCIDENTAL,0.2612655252892886,0.7387344747107114
+0.2612655252892886,0.7387344747107114
-KASAI-ORIENTAL,0.07622377139542966,0.9237762286045703
+0.07622377139542966,0.9237762286045703
-KATANGA,0.18062352012628255,0.8193764798737174
+0.18062352012628255,0.8193764798737174
-KINSHASA,0.07679244621346286,0.9232075537865372
+0.07679244621346286,0.9232075537865372
-MANIEMA,0.4611502742287561,0.5388497257712439
+0.4611502742287561,0.5388497257712439
-NORD-KIVU,0.11962561930536533,0.8803743806946347
+0.11962561930536533,0.8803743806946347
-ORIENTALE,0.16090483213325235,0.8390951678667476
+0.16090483213325235,0.8390951678667476
-SUD-KIVU,0.409646629226467,0.590353370773533
+0.409646629226467,0.590353370773533

assets/identified_category_distribution_by_province.svg

@@ -6,7 +6,7 @@
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-    <dc:date>2025-09-28T16:57:46.163844</dc:date>
+    <dc:date>2025-09-28T23:42:04.307504</dc:date>
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assets/names_letter_frequencies.csv

@@ -0,0 +1,27 @@
+letter,Male,Female
+a,0.1726871198212362,0.1780007719968084
+b,0.06275449167118631,0.05757115683434764
+c,0.002527913112031784,0.002525362815502787
+d,0.02639274743484273,0.025798130028588412
+e,0.060460557268468315,0.05992111228866155
+f,0.004168185425527368,0.005738163668905593
+g,0.03710295718248242,0.035944081768606244
+h,0.015744753594548896,0.016324638692088497
+i,0.07320872667180656,0.07954877144283247
+j,0.00442530712700423,0.004397881604276826
+k,0.06012485644271973,0.05719911396875115
+l,0.04930645065793003,0.04598845291218479
+m,0.08281339976187696,0.08014229460267776
+n,0.08138893330151427,0.08430430794896865
+o,0.06920807306069308,0.06452478894803111
+p,0.009832203366545821,0.009371006578405026
+q,5.0822826402147366e-05,8.43622136063042e-05
+r,0.009139850680293098,0.010064380634131025
+s,0.032639239825093015,0.034139532349508485
+t,0.0277669772899704,0.027953179679053274
+u,0.06917254296038988,0.06619473621457156
+v,0.0035449558612418576,0.006171217790567778
+w,0.013512780220408454,0.014295070954872152
+x,4.796818419701171e-05,1.6707334940670683e-05
+y,0.020592394840652214,0.020809516372185803
+z,0.01138579141093724,0.012971260356926069

assets/names_ngrams_summary.csv

@@ -0,0 +1,7 @@
+sex,position,2-grams,3-grams,4-grams
+female,prefix,"ka, ma, mu, mb, ng, ba, ki, lu, ts, bo","tsh, kab, ngo, mas, kas, kal, muk, kav, mbu, man","tshi, kavi, ngoy, kaso, ilun, mbuy, kaba, ntum, kavu, ngal"
+female,suffix,"ba, ga, la, ka, ma, da, go, ya, bo, na","nga, mba, ngo, nda, ala, mbo, ngu, ndo, mbe, mbu","anga, amba, ongo, umba, inga, ombo, unga, enga, anda, ungu"
+female,any,"ng, ka, mb, an, ba, ma, nd, ga, la, am","nga, mba, ang, ngo, amb, ong, nda, ala, mbo, eng","anga, amba, ongo, tshi, umba, inga, ombo, unga, anda, enga"
+male,prefix,"ka, mu, ma, ba, mb, ng, ki, lu, ts, bo","kab, tsh, kal, kas, muk, ngo, kam, mut, mul, mbu","tshi, ngoy, ilun, kaba, kaso, kamb, muke, kabe, kalo, muto"
+male,suffix,"ba, ga, la, go, ka, da, bo, le, di, ma","nga, mba, ngo, nda, ala, mbo, ngu, mbe, ndo, ele","amba, ongo, anga, umba, unga, ombo, anda, enga, onga, angu"
+male,any,"ng, ka, mb, ba, an, ma, mu, nd, am, al","nga, mba, ngo, amb, ang, ong, ala, nda, shi, mbo","amba, ongo, anga, tshi, umba, unga, ombo, anda, lung, enga"

assets/names_transition_probs.csv

@@ -1,29 +1,29 @@
-,^,a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z,$
+^,a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z,$
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assets/surnames_letter_frequencies.csv

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assets/surnames_ngrams_summary.csv

@@ -0,0 +1,7 @@
+sex,position,2-grams,3-grams,4-grams
+female,prefix,"ma, ch, be, na, an, sa, es, jo, ju, me","mar, cha, est, chr, gra, dor, sar, rut, ben, mer","mari, chri, esth, grac, sara, dorc, ruth, rach, naom, jean"
+female,suffix,"ne, ie, te, le, ce, ia, se, el, ah, th","ine, tte, lle, rah, nce, ene, nne, her, lie, rie","ette, line, tine, elle, ther, arie, ille, rcas, ruth, arah"
+female,any,"ne, in, el, an, ie, ri, ra, li, ar, er","ine, tte, ett, mar, ari, lle, lin, eli, the, ell","ette, line, ther, mari, tine, elle, rist, chri, ance, hris"
+male,prefix,"jo, je, pa, ch, ma, da, al, ju, be, fr","jea, jos, chr, pat, mar, jon, fra, dan, cha, ben","jean, chri, jose, jona, patr, fran, mich, emma, davi, dieu"
+male,suffix,"in, el, an, ck, on, re, ce, er, se, is","ean, tin, ick, ier, ard, uel, ert, ain, iel, ise","jean, stin, rick, bert, seph, than, oise, avid, ndre, tian"
+male,any,"an, er, el, ie, in, ri, is, on, en, re","ric, sti, jea, ean, tin, ris, ier, ist, ick, jos","jean, stin, rist, rick, chri, hris, usti, bert, jose, atha"

assets/surnames_transition_probs.csv

@@ -1,29 +1,29 @@
-,^,a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z,$
+^,a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z,$
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-y,0.0,0.07903953601739935,0.0008749671887304226,0.020399235028686423,0.025884029348899416,0.017196855117933077,0.0011899553766733747,0.0022049173156006648,0.00033248753171756057,0.011642063422621652,9.499643763358873e-05,0.0003999850005624789,0.07594465207554717,0.013214504456082897,0.04049848130695099,0.024181593190255365,0.006899741259702761,5.749784383085634e-05,0.01051710560853968,0.03773608489681637,0.0037698586303013637,0.0075047185730535105,0.028846418259315276,0.00024249090659100284,0.00047998200067497467,6.749746884491831e-05,0.0010774595952651777,0.5897028861417697
+0.0,0.07903953601739935,0.0008749671887304226,0.020399235028686423,0.025884029348899416,0.017196855117933077,0.0011899553766733747,0.0022049173156006648,0.00033248753171756057,0.011642063422621652,9.499643763358873e-05,0.0003999850005624789,0.07594465207554717,0.013214504456082897,0.04049848130695099,0.024181593190255365,0.006899741259702761,5.749784383085634e-05,0.01051710560853968,0.03773608489681637,0.0037698586303013637,0.0075047185730535105,0.028846418259315276,0.00024249090659100284,0.00047998200067497467,6.749746884491831e-05,0.0010774595952651777,0.5897028861417697
-z,0.0,0.40388373911101183,0.0005723698905517087,0.0004886084431538977,0.0008794951976770158,0.21811480902389993,2.792048246593701e-05,0.00011168192986374804,0.000991177127540764,0.20157192316283226,2.792048246593701e-05,0.00015356265356265356,0.0005584096493187402,0.0017589903953540316,0.0011168192986374804,0.07377987491623855,5.584096493187402e-05,2.792048246593701e-05,0.004844203707840071,6.980120616484253e-05,4.1880723698905516e-05,0.027669198123743577,6.980120616484253e-05,0.0018846325664507483,1.3960241232968505e-05,0.018092472637927185,0.004606879606879607,0.03858610676792495
+0.0,0.40388373911101183,0.0005723698905517087,0.0004886084431538977,0.0008794951976770158,0.21811480902389993,2.792048246593701e-05,0.00011168192986374804,0.000991177127540764,0.20157192316283226,2.792048246593701e-05,0.00015356265356265356,0.0005584096493187402,0.0017589903953540316,0.0011168192986374804,0.07377987491623855,5.584096493187402e-05,2.792048246593701e-05,0.004844203707840071,6.980120616484253e-05,4.1880723698905516e-05,0.027669198123743577,6.980120616484253e-05,0.0018846325664507483,1.3960241232968505e-05,0.018092472637927185,0.004606879606879607,0.03858610676792495
-$,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0
+0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0

assets/transition_comparisons.csv

@@ -1,3 +1,3 @@
-,l2,kl_mf,kl_fm,jsd,permutation_p_value
+category,l2,kl_mf,kl_fm,jsd,permutation_p_value
-names,0.3189041485139616,0.04320097944655348,0.0215380760498496,0.03236952774820154,0.979
+names,0.3189041485139616,0.04320097944655348,0.0215380760498496,0.03236952774820154,0.973
-surnames,1.2770018925640299,0.2936188220992242,0.23989460296618093,0.26675671253270256,0.001
+surnames,1.2770018925640299,0.2936188220992242,0.23989460296618093,0.26675671253270256,0.003

research/statistics/plots.py

@@ -1,6 +1,9 @@
+import numpy as np
+import pandas as pd
+import matplotlib.pyplot as plt
 import seaborn as sns
 
-from research.statistics.utils import LETTERS
+from research.statistics.utils import LETTERS, build_letter_frequencies
 
 
 def plot_transition_matrix(ax, df_probs, title=""):
@@ -12,4 +15,36 @@ def plot_transition_matrix(ax, df_probs, title=""):
         ax=ax
     )
     ax.set_title(title, fontsize=12)
-    return hm
+    return hm
+
+
+def plot_letter_frequencies(males, females, sort_values=False, title=None):
+    # Compute frequencies
+    L_m = build_letter_frequencies(males['name']).set_index("letter")["freq"]
+    L_f = build_letter_frequencies(females['name']).set_index("letter")["freq"]
+
+    # Combine into one DataFrame
+    df_plot = pd.DataFrame({"Male": L_m, "Female": L_f}).fillna(0).reset_index()
+    df_plot.to_csv(f"../assets/{title}_letter_frequencies.csv", index=False)
+
+    # Optional sorting
+    if sort_values:
+        df_plot = df_plot.sort_values("Male", ascending=False)
+
+    # Plot side-by-side bars
+    x = np.arange(len(df_plot))
+    w = 0.4
+    fig, ax = plt.subplots(figsize=(16, 6))
+    ax.bar(x - w/2, df_plot["Male"], width=w, label="Male", color="steelblue", alpha=0.8)
+    ax.bar(x + w/2, df_plot["Female"], width=w, label="Female", color="salmon", alpha=0.8)
+
+    ax.set_xticks(x)
+    ax.set_xticklabels(df_plot["letter"])
+    ax.set_ylabel("Frequency")
+    ax.set_xlabel("Letter")
+    ax.set_title(f"{title} - Letter Frequencies")
+    ax.legend()
+    ax.grid(axis="y", alpha=0.3)
+
+    plt.tight_layout()
+    plt.show()

research/statistics/utils.py

@@ -23,7 +23,7 @@ def normalize_letters(s):
     return s
 
 
-def identified_category_dist(df: pd.DataFrame) -> pd.DataFrame:
+def build_category_distribution(df: pd.DataFrame) -> pd.DataFrame:
     return (
         df.groupby("province")["identified_category"]
         .value_counts(normalize=True)  # get proportions
@@ -31,7 +31,7 @@ def identified_category_dist(df: pd.DataFrame) -> pd.DataFrame:
     )
 
 
-def explode_words_token(df: pd.DataFrame, source: str, target: str) -> pd.DataFrame:
+def build_words_token(df: pd.DataFrame, source: str, target: str) -> pd.DataFrame:
     # Normalize + split once (vectorized)
     s = df[source].fillna('').astype(str)
     s = (
@@ -55,12 +55,26 @@ def explode_words_token(df: pd.DataFrame, source: str, target: str) -> pd.DataFr
 
 
 def build_letter_frequencies(series: pd.Series) -> pd.DataFrame:
-    s = series.astype(str).str.lower().str.replace(r'[^a-z]', '', regex=True).str.cat(sep='')
+    # Normalize: lowercase, remove non-letters, concatenate all into one string
-    out = (
+    s = (
-        s.value_counts(normalize=False)
+        series.astype(str)
-        .reindex(list(LETTERS), fill_value=0)
+        .str.lower()
-        .rename_axis("letter").reset_index(name="count")
+        .str.replace(r'[^a-z]', '', regex=True)
+        .str.cat(sep='')
     )
+
+    # Convert string into Series of characters
+    chars = pd.Series(list(s))
+
+    # Count letters and ensure all letters are present
+    out = (
+        chars.value_counts(normalize=False)
+        .reindex(list(LETTERS), fill_value=0)
+        .rename_axis("letter")
+        .reset_index(name="count")
+    )
+
+    # Relative frequency
     total = out["count"].sum()
     out["freq"] = out["count"] / (total if total > 0 else 1)
     return out
@@ -209,3 +223,48 @@ def build_transition_comparisons(names_transitions: Dict[str, Any], surnames_tra
     }, index=["names", "surnames"])
 
     return out
+
+import pandas as pd
+from collections import Counter
+from typing import Literal
+
+
+def build_ngrams_count(
+        df: pd.DataFrame,
+        n: int,
+        where: Literal["any", "prefix", "suffix"] = "any",
+) -> pd.DataFrame:
+    # Normalize and clean to a–z
+    names = (
+        df["name"].astype(str)
+        .str.lower()
+        .str.replace(r"[^a-z]", "", regex=True)
+    )
+
+    ngrams = []
+    if where == "any":
+        for s in names:
+            L = len(s)
+            if L >= n:
+                ngrams.extend(s[i:i+n] for i in range(L - n + 1))
+    elif where == "prefix":
+        for s in names:
+            if len(s) >= n:
+                ngrams.append(s[:n])
+    elif where == "suffix":
+        for s in names:
+            if len(s) >= n:
+                ngrams.append(s[-n:])
+    else:
+        raise ValueError("where must be one of: 'any', 'prefix', 'suffix'")
+
+    counter = Counter(ngrams)
+
+    out = (
+        pd.DataFrame(counter.items(), columns=[f"{n}-gram", "count"])
+        .sort_values("count", ascending=False, kind="mergesort")
+        .reset_index(drop=True)
+    )
+    total = out["count"].sum()
+    out["freq"] = out["count"] / (total if total > 0 else 1)
+    return out